Maths-
General
Easy

Question

The maximum value of the expression open vertical bar square root of open parentheses sin squared space x plus 2 a squared close parentheses end root minus square root of open parentheses 2 a squared minus 1 minus cos squared space x close parentheses end root close vertical bar

where a and x are real numbers is

  1. square root of 3
  2. square root of 2
  3. 1
  4. square root of 5

hintHint:

In the question we will first simplify the given function then we will determine the maximum value.

The correct answer is: square root of 2


    open vertical bar square root of open parentheses sin squared space x plus 2 a squared close parentheses end root minus square root of open parentheses 2 a squared minus 1 minus cos squared space x close parentheses end root close vertical bar
equals open vertical bar square root of open parentheses sin squared space x plus 2 a squared close parentheses end root minus square root of open parentheses 2 a squared minus 1 minus 1 minus sin squared space x close parentheses end root close vertical bar
equals open vertical bar square root of open parentheses sin squared space x plus 2 a squared close parentheses end root minus square root of open parentheses sin squared space x plus 2 a squared minus 2 close parentheses end root close vertical bar
l e t space sin squared x plus 2 a squared space b e space y.
equals open vertical bar square root of y minus square root of y minus 2 end root close vertical bar
S i n c e space b o t h space t h e space t e r m s space a r e space p o s i t i v e comma space t h e space g i v e n space f u n c t i o n space w i l l space h a v e space t h e space m a x i m u m space v a l u e space w h e n space y equals 2
i. e. comma space square root of y minus 2 end root equals 0
N o w comma space open vertical bar square root of y minus square root of y minus 2 end root close vertical bar equals square root of 2

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