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Question

The value of sin π4+θ-cos π4-θ is
(a) 2 cosθ
(b) 2 sinθ
(c) 1
(d) 0

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Solution

sinπ4+θ-cosπ4-θ=sinπ4 cosθ+cosπ4 sinθ-cosπ4cosθ+sinπ4 sinθUsing identities:sin(a+b)=sina cosb + cosa sinbcos(a-b)=cosa cosb + sina sinb=12cosθ+12sinθ-12cosθ-12sinθ=0i.e sinπ4+θ-cosπ4-θ=0.Hence, the correct answer is option D.

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