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Question

Solve: sinxtanx1=tanxsinx.

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Solution

sinx tanx-1 = tanx - sinx
sinxsinxcosx1=sinxcosxsinx
sin2xcosxcosx=sinx[1cosx]cosx
sin2xcosx=sinxsinxcosx
sin2sinxcosx+sinxcosx=0
sinx[sinx1]+cosx[sinx1]=0
[sinx+cosx][sinx1]=0
[sinx+cosx=0] or [sinx=1]
then x=(2n+1)π2

1208180_1361405_ans_c34f70699aec4cf89992b41a3ade762a.JPG

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