Maths-
General
Easy

Question

The minimum and maximum values of sin to the power of 4 x plus cos to the power of 4 space x are

  1. 1 half comma 3 over 2
  2. 1 half comma space 1
  3. 1 comma 3 over 2
  4. 1,2

Hint:

In this question, we have to find the maximum and minimum value of the given equation. For that first we will simplify the trigonometric function, later assuming the possible range of the trigonometric function obtained we can find the maximum and minimum value.

The correct answer is: 1 half comma space 1


    space space space space space sin to the power of 4 x plus cos to the power of 4 space x
equals open parentheses sin squared x close parentheses squared plus open parentheses cos squared x close parentheses squared
equals open parentheses sin squared x plus cos squared x close parentheses squared minus 2 sin squared x. cos squared x
equals 1 minus fraction numerator sin squared space 2 x over denominator 2 end fraction
F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma sin space 2 x equals 0
S o comma space f left parenthesis x right parenthesis equals 1 minus 0 over 2 equals 1
F o e space m i n i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space sin space 2 x space equals 1
S o comma space f left parenthesis x right parenthesis equals 1 minus 1 squared over 2 equals 1 half

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