Question

Comine the facts that d/dx sinx=cosx and that sin(x+pie/2)=cosx to show d/dxcosx=-sinx?

Answer 1

\[\frac d{dx}\cos x\]\[=\frac d{dx}\sin\left(x+\frac\pi2\right)\]\[=\cos\left(x+\frac\pi2\right)\]\[=\cos x\cos\frac\pi2-\sin x\sin\frac\pi2\]\[=\cos x\cdot0-\sin x\cdot1\]\[=-\sin x\]

Answer 2

thankyou! :)