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Question Number 34382 by rashedul last updated on 05/May/18

$$\mathrm{how}\mathrm{do}\mathrm{i}\mathrm{prove}$$$${\int }_{\mathrm{o}}^{\mathrm{t}}\cos 2(\omega \mathrm{t}+\alpha )\mathrm{dt}=0$$

Answered by tanmay.chaudhury50@gmail.com last updated on 05/May/18

$$=\frac{\mid sin(2wt+2\alpha )\underset{0}{\stackrel{T}{\mid }}}{2w}$$$$=\frac{sin(2wT+2\alpha )-sin\left(2\alpha \right)}{2w}$$$$w=\frac{2\mathrm{\Pi }}{T}so$$$$=\frac{sin(4\mathrm{\Pi }+2\alpha )-sin2\alpha }{2\omega }$$$$=\frac{sin2\alpha -sin2\alpha }{2w}$$$$=0$$$$ithinkupperlimigofintregalisTwhereT$$$$T=2\mathrm{\Pi }/w$$

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