Question #49ba0

1 Answer
P dilip_k
Jan 23, 2017

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

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