Maths-
General
Easy

Question

The minimum and maximum values of sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses are

  1. -1,1
  2. negative 1 half comma 1 half
  3. negative 3 over 2 comma 3 over 2
  4. negative 1 fourth comma 1 fourth

Hint:

In this question we have to find the minimum and maximum value of the given function. For this we will first simplify the equation using some trigonometric identities then we will assume the range of the trigonometric function and later put it in f(x) to find the maximum and minimum value.

The correct answer is: negative 1 half comma 1 half


    sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses
equals sin squared x minus sin squared straight pi over 4
equals fraction numerator 1 minus cos 2 x over denominator 2 end fraction minus open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared
equals 1 half minus fraction numerator cos 2 x over denominator 2 end fraction minus 1 half
equals negative 1 half cos 2 x
F o r 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 cos 2 x equals 1
f left parenthesis x right parenthesis equals negative 1 half cross times 1 equals fraction numerator negative 1 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 space cos 2 x equals negative 1
f left parenthesis x right parenthesis equals negative 1 half cross times negative 1 equals 1 half
S o comma space sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses element of open square brackets fraction numerator negative 1 over denominator 2 end fraction comma 1 half close square brackets

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