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Question

If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =
(a) 0
(b) 5
(c) 1
(d) None of these

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Solution

(a) 0

3 sin x +4 cos x=535sin x+45cos x=1Let cos α=35 and sin α=45. cos α sin x+sinαcos x=1 sin α+x=sinπ2α+x=π2x=π2-α ....(1)We have to find the value of 4 sin x-3 cos x. 4 sinπ2-α -3 cosπ2-α ...{From eq (1)} =4cos α-3sinα =4 × 35-3×45 cos α=35 and sin α=45 =0

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