Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

In $straight triangle A B C sum a cubed Sin space left parenthesis B minus C right parenthesis$ =

0
1
2
3

hint Hint:

In this question, we have to find the value of $sum a cubed Sin space left parenthesis B minus C right parenthesis$ . For this we will use sine rule, $fraction numerator sin space A over denominator a end fraction equals fraction numerator sin space B over denominator b end fraction equals fraction numerator sin space C over denominator c end fraction equals k$ and cosine rule, $cos space A equals fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction comma space cos space B equals fraction numerator c squared plus a squared minus b squared over denominator 2 a c end fraction comma space cos space C equals fraction numerator a squared plus b squared minus c squared over denominator 2 a b end fraction$ .

The correct answer is: 0

$B y space sin space r u l e comma space fraction numerator sin space A over denominator a end fraction equals fraction numerator sin space B over denominator b end fraction equals fraction numerator sin space C over denominator c end fraction equals k B y space cos i n e space r u l e comma cos space A equals fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction comma space cos space B equals fraction numerator c squared plus a squared minus b squared over denominator 2 a c end fraction comma space cos space C equals fraction numerator a squared plus b squared minus c squared over denominator 2 a b end fraction sum a cubed space sin space left parenthesis B minus C right parenthesis equals a cubed left parenthesis sin space B. cos space C minus cos space B. sin space C right parenthesis plus b cubed left parenthesis sin space C. cos space A minus cos space C. sin space A right parenthesis plus c cubed left parenthesis sin space A. cos space B minus cos space A. sin space B right parenthesis equals a cubed open parentheses k b cross times fraction numerator a squared plus b squared minus c squared over denominator 2 a b end fraction minus k c cross times fraction numerator c squared plus a squared minus b squared over denominator 2 a c end fraction close parentheses plus b cubed open parentheses k c cross times fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction minus k a cross times fraction numerator a squared plus b squared minus c squared over denominator 2 a b end fraction close parentheses plus c cubed open parentheses k a cross times fraction numerator c squared plus a squared minus b squared over denominator 2 a c end fraction minus k b cross times fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction close parentheses equals a cubed cross times fraction numerator 1 over denominator 2 a end fraction open parentheses a squared plus b squared minus c squared minus c squared minus a squared plus b squared close parentheses plus b cubed cross times fraction numerator 1 over denominator 2 b end fraction open parentheses b squared plus c squared minus a squared minus a squared minus b squared plus c squared close parentheses plus c cubed cross times fraction numerator 1 over denominator 2 c end fraction open parentheses c squared plus a squared minus b squared minus b squared minus c squared plus a squared close parentheses equals a squared cross times 1 half cross times 2 open parentheses b squared minus c squared close parentheses plus b squared cross times 1 half cross times 2 open parentheses c squared minus a squared close parentheses plus c squared cross times 1 half cross times open parentheses a squared minus b squared close parentheses equals a squared b squared minus a squared c squared plus b squared c squared minus a squared b squared plus a squared c squared minus b squared c squared equals 0$

Related Questions to study

In $straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis equals$

In $straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis equals$

If the period of $fraction numerator cos space left parenthesis sin space left parenthesis n x right parenthesis right parenthesis over denominator tan space left parenthesis x divided by n right parenthesis end fraction comma n element of N$ is $6 pi$ then n=

If the period of $fraction numerator cos space left parenthesis sin space left parenthesis n x right parenthesis right parenthesis over denominator tan space left parenthesis x divided by n right parenthesis end fraction comma n element of N$ is $6 pi$ then n=

Let $f left parenthesis x right parenthesis equals cos space square root of p x$ where $p equals left square bracket a right square bracket$ where [ ] is the integral part of x. If the period of f(x) is $pi$ , then $a element of$

Let $f left parenthesis x right parenthesis equals cos space square root of p x$ where $p equals left square bracket a right square bracket$ where [ ] is the integral part of x. If the period of f(x) is $pi$ , then $a element of$

parallel

Which of the following options is correct for the object having a straight line motion represented by the following graph

Which of the following options is correct for the object having a straight line motion represented by the following graph

physics-General

A body begins to walk eastward along a street in front of his house and the graph of his position from home is shown in the following figure. His average speed for the whole time interval is equal to

A body begins to walk eastward along a street in front of his house and the graph of his position from home is shown in the following figure. His average speed for the whole time interval is equal to

physics-General

A particle is moving with uniform acceleration along a straight line. The average velocity of the particle from $P$ to $Q$ is $8 m s to the power of negative 1 end exponent$ and that from $Q$ to $S$ is $12 m s to the power of negative 1 end exponent$ . If $Q S minus P Q$ , then the average velocity from $P$ to $S$ is

A particle is moving with uniform acceleration along a straight line. The average velocity of the particle from $P$ to $Q$ is $8 m s to the power of negative 1 end exponent$ and that from $Q$ to $S$ is $12 m s to the power of negative 1 end exponent$ . If $Q S minus P Q$ , then the average velocity from $P$ to $S$ is

physics-General

parallel

i)
ii)
iii)
iv) $Me minus identical to negative straight H rightwards arrow with text dil.H end text subscript 2 SO subscript 4 plus Hg to the power of 2 plus end exponent on top$
Which of the statements are correct?

i)
ii)
iii)
iv) $Me minus identical to negative straight H rightwards arrow with text dil.H end text subscript 2 SO subscript 4 plus Hg to the power of 2 plus end exponent on top$
Which of the statements are correct?

chemistry-General

A body is travelling in a straight line with a uniformly increasing speed. Which one of the plot represents the changes in distance (s) travelled with time ( $t$ )

A body is travelling in a straight line with a uniformly increasing speed. Which one of the plot represents the changes in distance (s) travelled with time ( $t$ )

physics-General

The value of integer n for which the function $f left parenthesis x right parenthesis equals fraction numerator sin begin display style space end style n x over denominator sin begin display style space end style left parenthesis x divided by n right parenthesis end fraction$ has $4 pi$ as its period is

The value of integer n for which the function $f left parenthesis x right parenthesis equals fraction numerator sin begin display style space end style n x over denominator sin begin display style space end style left parenthesis x divided by n right parenthesis end fraction$ has $4 pi$ as its period is

parallel

$cos squared space open parentheses 60 to the power of ring operator plus x close parentheses minus cos squared space open parentheses 60 to the power of ring operator minus x close parentheses element of open square brackets negative m over 2 comma m over 2 close square brackets not stretchy rightwards double arrow straight m equals$

$cos squared space open parentheses 60 to the power of ring operator plus x close parentheses minus cos squared space open parentheses 60 to the power of ring operator minus x close parentheses element of open square brackets negative m over 2 comma m over 2 close square brackets not stretchy rightwards double arrow straight m equals$

$cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of$

$cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of$

The effective capacitance between points $X$ and $Y$ shown in figure. Assuming $C subscript 2 end subscript equals 10 blank mu$ F and that outer capacitors are all $4 blank mu$ F is

The effective capacitance between points $X$ and $Y$ shown in figure. Assuming $C subscript 2 end subscript equals 10 blank mu$ F and that outer capacitors are all $4 blank mu$ F is

physics-General

parallel

The four capacitors, each of 25 $mu$ F are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

The four capacitors, each of 25 $mu$ F are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

physics-General

For the circuit shown in figure the charge on 4 $mu$ F capacitor is

For the circuit shown in figure the charge on 4 $mu$ F capacitor is

physics-General

The minimum and maximum values of $sin to the power of 4 x plus cos to the power of 4 space x$ are

The minimum and maximum values of $sin to the power of 4 x plus cos to the power of 4 space x$ are

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.