How do you prove #(sin x+ 1) / (cos x + cot x) = tan x#?

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Answer 1 · 2018-06-23T06:31:11

Below

#(sinx+1)/(cosx+cotx)=tanx#

LHS
#(sinx+1)/(cosx+cotx)#

=#(sinx+1)/(cosx+cosx/sinx)#

=#(sinx+1)/((sinxcosx+cosx)/sinx)#

=#(sinx^2+sinx)/(sinxcosx+cosx)#

=#(sinx(sinx+1))/(cosx(sinx+1))#

=#(sinx cancel((sinx+1)))/(cosx cancel((sinx+1)))#

=#sinx/cosx#

=#tanx#

=RHS

Therefore, #(sinx+1)/(cosx+cotx)=tanx#