Question #49ba0

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Answer 1 · 2017-01-23T05:57:52

To prove

$sinx (1+tanx) + cosx (1+cotx) = (sinx + cosx) / (sinxcosx$

$LHS=sinx (1+tanx) + cosx (1+cotx)$

$=sinx/cosx (cosx+cosx*tanx)+ cosx/sinx (sinx+sinx*cotx)$

$=sinx/cosx (cosx+cosx*sinx/cosx)+ cosx/sinx (sinx+sinx*cosx/sinx)$

$=sinx/cosx (cosx+sinx)+ cosx/sinx (sinx+cosx)$

$=(sinx+cosx)(sinx/cosx + cosx/sinx )$

$=(sinx+cosx)((sin^2x+ cos^2x)/(sinxcosx ))$

$=(sinx+cosx)/(sinxcosx )=RHS$

Proved