Question

$Prove:\ \textless \ br /\ \textgreater \ \ \textless \ br /\ \textgreater \ \bf{\frac{d( \ { \sin}^{n}x . \cos \: n \: x ) }{dn} = n \: { \sin }^{n + 1} \: \cos( n + 1)}$
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Answer 1

Step-by-step explanation:

y = sinn x cos nx

dy/dx = n sinn-1 x cos x cos nx – sinn x sin nx (n)

= n sinn-1 x(cos x cos nx – sin x sin nx)

= n sinn-1x(cos (nx+x))

= n sinn-1x(cos (n+1)x)