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Maths-

General

Easy

Question

For any real $theta$ , the maximum value of $cos squared space left parenthesis cos space theta right parenthesis plus sin squared space left parenthesis sin space theta right parenthesis$ is

1
$1 + \sin^{2} 1$
$1 + \cos^{2} 1$

hint Hint:

To find the maximum value of the given function we will first determine the value of $theta$ when the function will be maximum.

The correct answer is: $1 plus sin squared space 1$

As cos is a decreasing function and sin is an increasing function so the function $cos squared space left parenthesis cos space theta right parenthesis plus sin squared space left parenthesis sin space theta right parenthesis$ is maximum when $theta$ = $90 degree$ .
So, the maximum value of $cos squared space left parenthesis cos space theta right parenthesis plus sin squared space left parenthesis sin space theta right parenthesis$ = $cos squared space left parenthesis cos space 90 degree right parenthesis plus sin squared space left parenthesis sin space 90 degree right parenthesis equals cos squared 0 plus sin squared 1 equals 1 plus sin squared 1$

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