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Question
sinmx . cosnx
Solution
Let y = sinmx . cosnx
∴ `"dy"/"dx" = "d"/"dx" [(sin x)^"m" * (cos x)^"n"]`
= `(sin x)^"m" "d"/"dx" (cos x)^"n" + (cos x)^"n" "d"/"dx" (sin x)^"m"`
= `(sin x)^"m" "n"(cos x)^("n" - 1) "d"/"dx" (cos x) + (cos x)^"n" "m"(sin x)^("m" - 1) "d"/"dx" (sin x)`
= `(sin x)^"m" "n"(cos x)^("n" - 1) (- sin x) + (cos x)^"n" "m"(sin x)^("m" - 1) cos x`
= sinm x cosn x[–n tan x + m cot x]
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