Maths-
General
Easy
Question
If 
 and 
 then 
- 1
- 3
- 4
- 5
Hint:
In the question we will simplify the given equations using some trigonometric identities.
The correct answer is: 4
on multiplying equation 1 and 2,
Related Questions to study
Maths-
The maximum value of 
 under the restrictions 
 and 
 is
Given,Â
The maximum value of  under the restrictions  and  is
Maths-General
Given,Â
Maths-
Let 
 be two sets. Then
Given two setsÂ
Let  be two sets. Then
Maths-General
Given two setsÂ
Maths-
If 
 then 
 is
If  then  is
Maths-General
physics-
A long cylindrical tube carries a highly polished piston and has a side opening. A tuning fork of frequency n is sounded at the sound heard by the listener charges if the piston is moves in or out. At a particular position of the piston is moved through a distance of 9 cm, the intensity of sound becomes minimum, if the speed of sound is 360 m/s, the value of n is
When piston moves a distance
, path difference change by 2 xs.
the path difference between maxima and consecutive minima=
∴
Or
λ=4x=4×9 cm=36cm=0.36m
, path difference change by 2 xs.the path difference between maxima and consecutive minima=∴
Or
λ=4x=4×9 cm=36cm=0.36m
A long cylindrical tube carries a highly polished piston and has a side opening. A tuning fork of frequency n is sounded at the sound heard by the listener charges if the piston is moves in or out. At a particular position of the piston is moved through a distance of 9 cm, the intensity of sound becomes minimum, if the speed of sound is 360 m/s, the value of n is
physics-General
When piston moves a distance, path difference change by 2 xs.
the path difference between maxima and consecutive minima=
∴
Or
λ=4x=4×9 cm=36cm=0.36m
, path difference change by 2 xs.the path difference between maxima and consecutive minima=∴
Or
λ=4x=4×9 cm=36cm=0.36m
Maths-
The value of 
The value ofÂ
Maths-General
Maths-
For any real 
, the maximum value of 
 is
As cos is a decreasing function and sin is an increasing function so the function  is maximum when =
.
So, the maximum value ofÂÂ =Â 
 is maximum when =.So, the maximum value ofÂ
 = For any real , the maximum value of  is
Maths-General
As cos is a decreasing function and sin is an increasing function so the function  is maximum when =.
So, the maximum value ofÂÂ =Â
 is maximum when =.So, the maximum value ofÂ
 = 
chemistry-
Identify A and B
With H2 / pd / CaCO3 - is addition of ‘H’ know is oxidizing agent
Identify A and B
chemistry-General
With H2 / pd / CaCO3 - is addition of ‘H’ know is oxidizing agent
Maths-
If 
 then sin (A-B) =
GIVEN-
​  √2 cos A = cos B + cos3 B..... equation 1
∴    cos A = 1/√2 (cos B + cos3 B) ........ (Dividing both sides by √2)
TO FIND-
Sin (A - B)
SOLUTION-
We know that-
Sin (A - B) = (Sin A * Cos B) - (Cos A * Sin B)
∴ Sin (A - B) = [1/√2 (sin B - sin3 B) * cos B] - [1/√2 (cos B + cos3 B) * sin B] ...... (From Equations i & ii)
∴ Sin (A - B) = [1/√2 * (sin B Cos B - sin3 B Cos B)] - [1/√2 * (sin B cos B + cos3 B * sin B)]
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin3 B Cos B - (1/√2 sin B cos B + 1/√2 cos3 B * sin B)
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin3 B Cos B - 1/√2 sin B cos B - 1/√2 cos3 B * sin B
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin3 B Cos B - 1/√2 sin B cos B - 1/√2 cos3 B * sin B
∴ Sin (A - B) = -1/√2 sin3 B Cos B - 1/√2 cos3 B * sin B
∴ Sin (A - B) = -1/√2 sin B Cos B (sin2 B +cos2 B)
          = -1/2√2 sin2B
Now squaring and adding equation 1 and 2 we get
​  √2 cos A = cos B + cos3 B..... equation 1
∴    cos A = 1/√2 (cos B + cos3 B) ........ (Dividing both sides by √2)
√2 sin A = sin B - sin3 B..... equation 2
∴    sin A = 1/√2 (sin B - sin3 B) ........ (Dividing both sides by √2)TO FIND-
Sin (A - B)
SOLUTION-
We know that-
Sin (A - B) = (Sin A * Cos B) - (Cos A * Sin B)
∴ Sin (A - B) = [1/√2 (sin B - sin3 B) * cos B] - [1/√2 (cos B + cos3 B) * sin B] ...... (From Equations i & ii)
∴ Sin (A - B) = [1/√2 * (sin B Cos B - sin3 B Cos B)] - [1/√2 * (sin B cos B + cos3 B * sin B)]
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin3 B Cos B - (1/√2 sin B cos B + 1/√2 cos3 B * sin B)
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin3 B Cos B - 1/√2 sin B cos B - 1/√2 cos3 B * sin B
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin3 B Cos B - 1/√2 sin B cos B - 1/√2 cos3 B * sin B
∴ Sin (A - B) = -1/√2 sin3 B Cos B - 1/√2 cos3 B * sin B
∴ Sin (A - B) = -1/√2 sin B Cos B (sin2 B +cos2 B)
          = -1/2√2 sin2B
Now squaring and adding equation 1 and 2 we get
If  then sin (A-B) =
Maths-General
GIVEN-
​  √2 cos A = cos B + cos3 B..... equation 1
∴    cos A = 1/√2 (cos B + cos3 B) ........ (Dividing both sides by √2)
TO FIND-
Sin (A - B)
SOLUTION-
We know that-
Sin (A - B) = (Sin A * Cos B) - (Cos A * Sin B)
∴ Sin (A - B) = [1/√2 (sin B - sin3 B) * cos B] - [1/√2 (cos B + cos3 B) * sin B] ...... (From Equations i & ii)
∴ Sin (A - B) = [1/√2 * (sin B Cos B - sin3 B Cos B)] - [1/√2 * (sin B cos B + cos3 B * sin B)]
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin3 B Cos B - (1/√2 sin B cos B + 1/√2 cos3 B * sin B)
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin3 B Cos B - 1/√2 sin B cos B - 1/√2 cos3 B * sin B
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin3 B Cos B - 1/√2 sin B cos B - 1/√2 cos3 B * sin B
∴ Sin (A - B) = -1/√2 sin3 B Cos B - 1/√2 cos3 B * sin B
∴ Sin (A - B) = -1/√2 sin B Cos B (sin2 B +cos2 B)
          = -1/2√2 sin2B
Now squaring and adding equation 1 and 2 we get
​  √2 cos A = cos B + cos3 B..... equation 1
∴    cos A = 1/√2 (cos B + cos3 B) ........ (Dividing both sides by √2)
√2 sin A = sin B - sin3 B..... equation 2
∴    sin A = 1/√2 (sin B - sin3 B) ........ (Dividing both sides by √2)TO FIND-
Sin (A - B)
SOLUTION-
We know that-
Sin (A - B) = (Sin A * Cos B) - (Cos A * Sin B)
∴ Sin (A - B) = [1/√2 (sin B - sin3 B) * cos B] - [1/√2 (cos B + cos3 B) * sin B] ...... (From Equations i & ii)
∴ Sin (A - B) = [1/√2 * (sin B Cos B - sin3 B Cos B)] - [1/√2 * (sin B cos B + cos3 B * sin B)]
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin3 B Cos B - (1/√2 sin B cos B + 1/√2 cos3 B * sin B)
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin3 B Cos B - 1/√2 sin B cos B - 1/√2 cos3 B * sin B
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin3 B Cos B - 1/√2 sin B cos B - 1/√2 cos3 B * sin B
∴ Sin (A - B) = -1/√2 sin3 B Cos B - 1/√2 cos3 B * sin B
∴ Sin (A - B) = -1/√2 sin B Cos B (sin2 B +cos2 B)
          = -1/2√2 sin2B
Now squaring and adding equation 1 and 2 we get
chemistry-
Observer the following reactions and predict the nature of A and B
Conceptual
Observer the following reactions and predict the nature of A and B
chemistry-General
Conceptual
chemistry-
on ozonolysis gives
on ozonolysis gives
chemistry-General
chemistry-
Which of the following reactions will yield 2, 2-dibromopropane?
Which of the following reactions will yield 2, 2-dibromopropane?
chemistry-General
Maths-
If 
 then 
 is equal to
If  then  is equal to
Maths-General
Maths-
If 
 where 
 being an acute angle then 
 
 is equal to
If  where  being an acute angle then   is equal to
Maths-General
maths-
Let A,B,CÂ be three angles such that 
 and 
. Then, all possible values of P such that A,B,C are the angles of a triangle is
Let A,B,C be three angles such that  and . Then, all possible values of P such that A,B,C are the angles of a triangle is
maths-General
chemistry-
is an example for
is an example for
chemistry-General
