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Question
The value of `cos(pi/4 + x) - cos(pi/4 - x)` is ______.
Options
`sqrt(2) sin x`
`- sqrt(2) sin x`
`sqrt(2) cos x`
`- sqrt(2) cos x`
MCQ
Fill in the Blanks
Solution
The value of `cos(pi/4 + x) - cos(pi/4 - x)` is `- sqrt(2) sin x`.
Explanation:
`cos(pi/4 + x) - cos(pi/4 - x)`
= `cos pi/4 cos x - sin pi/4 sin x - cos pi/4 cos x - sin pi/4 sin x`
= `- 2 sin pi/4 sin x`
= `- 2/sqrt(2) sin x`
= `- sqrt(2) sin x`
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