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Question

tan38° – cot22° = ?

(A)1/2 cosec38°sec22°

(B) 2sin22°cos38°

(C) –1/2 cosec22°sec38°

(D) none of these

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Solution

OPtion (C)

LHS

=tan38°-cot22°

=(sin38°/cos38°)-(cos22°/sin22°)

=(sin38°sin22°-cos38°cos22°)/(cos38°)(sin22°)

=-cos(38°+22°)(sec38°)(cosec22°)

=-cos60°cosec22°sec38°

=-½cosec22°sec38°

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