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Question

Prove x=nπ+(1)n.π2 or x=(nπ+3π4), where m, nI

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Solution

The given equation becomes

(sin x -1)(sin x +cos x)=0

sin x=1 or tan x =-1

sin x=sin π2 or tan x=tan3π4

x=nπ+(1)nπ2 or x=mπ+3π4, where m, nI.


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