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Maths-

General

Easy

Question

$sin squared space x plus cos to the power of 4 space x element of$

$[\frac{1}{4}, \frac{1}{2}]$
$[\frac{3}{4}, 1]$
$[- 1, - \frac{3}{4}]$
$[- \frac{3}{4}, \frac{3}{4}]$

hint Hint:

In this question, we have to find the range of the given function. Firstly, we will simplify to find the maximum and minimum value of the function and later write it in the form of range.

The correct answer is: $open square brackets 3 over 4 comma 1 close square brackets$

$sin squared space x plus cos to the power of 4 space x equals sin squared x plus cos squared x left parenthesis 1 minus sin squared x right parenthesis equals sin squared x plus cos squared x minus sin squared x. cos squared x equals 1 minus sin squared x. cos squared x S o comma space 1 minus sin squared x. cos squared x less or equal than 1 A g a i n comma space sin squared space x plus cos to the power of 4 space x equals 1 minus cos squared x plus cos to the power of 4 x equals open parentheses cos squared x minus 1 half close parentheses squared plus 3 over 4 S o comma space 1 minus sin squared x. cos squared x greater or equal than 3 over 4 T h e r e f o r e comma space sin squared space x plus cos to the power of 4 space x element of open square brackets 3 over 4 comma 1 close square brackets$

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