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Question
The value of sin(45° + θ) - cos(45° - θ) is ______.
Options
2cosθ
2sinθ
1
0
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Solution
The value of sin(45° + θ) - cos(45° - θ) is 0.
Explanation:
Given expression is sin(45° + θ) - cos(45° - θ)
sin(45° + θ) = sin45° cosθ + cos45° sinθ
= `1/sqrt(2) cos theta + 1/sqrt(2) sin theta`
cos(45° - θ) = cos45° cosθ + sin45° sinθ
= `1/sqrt(2) cos theta + 1/sqrt(2) sin theta`
sin(45° + θ) - cos(45° - θ)
= `1/sqrt(2) costheta + 1/sqrt(2) sintheta - 1/sqrt(2) cos theta - 1/sqrt(2) sin theta`
= 0.
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