Maths-

General

Easy

Question

$4 sin to the power of 4 space x plus cos to the power of 4 space x equals 1$ if

$x = n π$
$x = n π \pm \frac{1}{2} \cos^{- 1} (\frac{1}{5})$
$x = \frac{n π}{2}$
$none of these, (n \in I)$

Hint:

In this question, we have given, $4 sin to the power of 4 space x plus cos to the power of 4 space x equals 1$ . Solve this equation and find the general solution for x.

The correct answer is: $x equals n pi$

Here, we have to find the the general solution for x
Firstly, we have given equation,
$4 sin to the power of 4 space x plus cos to the power of 4 space x equals 1$

$equals greater than 4 s i n to the power of 4 x equals 1 minus c o s to the power of 4 x equals left parenthesis 1 minus c o s squared x right parenthesis left parenthesis 1 plus c o s squared x right parenthesis equals s i n squared x left parenthesis 2 minus s i n squared x right parenthesis equals greater than 4 s i n to the power of 4 x equals s i n squared x left parenthesis 2 minus s i n squared x right parenthesis equals greater than 4 s i n to the power of 4 x equals 2 s i n squared x minus s i n to the power of 4 x equals greater than 5 s i n to the power of 4 x equals 2 s i n squared x equals greater than 5 s i n to the power of 4 x minus 2 s i n squared x equals 0 equals greater than s i n squared x space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket 5 s i n squared x minus 2 right square bracket equals 0$

So we can write,
$S i n squared x equals 0 space space a n d space space 5 s i n squared x minus 2 equals 0$
x = n π and sin²x = $2 over 5$
-2 sin² x = $fraction numerator negative 4 over denominator 5 end fraction$
1 – 2 sin² x = $1 fifth$
Cos 2x = $1 fifth$
2x = 2n π ± cos^-1 ( $1 fifth$ )
X = n π ± $1 half$ cos^-1 ( $1 fifth$ )
Therefore, the correct answer is x = n π and x = n π ± $1 half$ cos^-1 ( $1 fifth$ ). Both options will correct.

In this question, we have to find the general solution of x. Here more than one option will correct. Remember the rules for finding the general solution.

Number of ordered pairs (a, x) satisfying the equation $sec squared space left parenthesis a plus 2 right parenthesis x plus a squared minus 1 equals 0 semicolon minus pi less than x less than pi$ is

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If $fraction numerator sin cubed space theta minus cos cubed space theta over denominator sin space theta minus cos space theta end fraction minus fraction numerator cos begin display style space end style theta over denominator square root of 1 plus cot 2 space theta end root end fraction minus 2 tan space theta cot space theta equals negative 1$ ,then

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The most general solution of the equations $tan space theta equals negative 1 comma cos space theta equals 1 divided by square root of 2$ is

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Let S = $open curly brackets x element of left parenthesis negative pi comma pi right parenthesis colon x not equal to 0 comma plus-or-minus pi over 2 close curly brackets$ The sun of all distinct solution of the equation $square root of 3 sec space x plus cosec space x plus 2 left parenthesis tan space x minus cot space x right parenthesis equals 0$

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A wave motion has the function $y equals a subscript 0 end subscript sin invisible function application left parenthesis omega t minus k x right parenthesis.$ The graph in figure shows how the displacement $y$ at a fixed point varies with time $t.$ Which one of the labelled points shows a displacement equal to that at the position $x equals fraction numerator pi over denominator 2 k end fraction$ at time $t equals 0$

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For $x element of left parenthesis 0 comma pi right parenthesis$ , the equation $sin space x plus 2 sin space 2 x minus sin space 3 x equals 3$ has

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if

In this question, we have given, . Solve this equation and find the general solution for x.

The correct answer is:

Here, we have to find the the general solution for xFirstly, we have given equation,So we can write,x = n π and sin2x = -2 sin2 x = 1 – 2 sin2 x = Cos 2x = 2x = 2n π ± cos-1 ()X = n π ± cos-1 () Therefore, the correct answer is x = n π and x = n π ± cos-1 (). Both options will correct.

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$4 sin to the power of 4 space x plus cos to the power of 4 space x equals 1$ if

In this question, we have given, $4 sin to the power of 4 space x plus cos to the power of 4 space x equals 1$ . Solve this equation and find the general solution for x.

The correct answer is: $x equals n pi$

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Number of ordered pairs (a, x) satisfying the equation $sec squared space left parenthesis a plus 2 right parenthesis x plus a squared minus 1 equals 0 semicolon minus pi less than x less than pi$ is

Which compound does not give $N H subscript 3$ on heating?

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