Maths-
General
Easy

Question

cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of

  1. [negative 1 half comma 1 half]
  2. [1 half comma 1]
  3. [1 half comma 3 over 2]
  4. [3 over 2 comma 2]

Hint:

In this question, we have to find the maximum and minimum value of the function given. For that first we will simplify the given trigonometric function, then we will assume the possible range of the function using which we can find the maximum and minimum values.

The correct answer is: [1 half comma 3 over 2]


    space space space space cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses
equals open parentheses cos space open parentheses 60 plus x close parentheses plus cos open parentheses 60 minus x close parentheses close parentheses squared minus 2 cos space open parentheses 60 minus x close parentheses. cos space open parentheses 60 plus x close parentheses
equals open parentheses 2. cos space 60. cos space x close parentheses squared minus open parentheses cos space 2 x space plus cos space 120 space close parentheses
equals 4 cross times 1 fourth cross times cos squared x minus cos space 2 x space minus open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses
equals cos squared x minus cos space 2 x plus 1 half
equals cos squared x minus 2 cos squared x plus 1 plus 1 half
equals 3 over 2 minus cos squared x
    For maximum value of f (x), cos squared x equals 0
    f (x)=3 over 2 minus 0 equals 3 over 2
    For minimum value of f (x), cos squared x equals 1
    f (x)=3 over 2 minus 1 equals 1 half
    So, cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of open square brackets 1 half comma 3 over 2 close square brackets.

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