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
  2. 1 plus sin squared space 1
  3. 1 plus cos squared space 1

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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