Verify the identity:

Question

(tanx+1)/(secx+cscx) = sinx

Answer 1

multiply through by sec+csc to get

tan+1 = sin(sec+csc)
= sinsec + sincsc
= tan + 1

Answer 2

LS= (sinx/cosx + 1)/(1/cosx + 1/sinx)
= [(sinx + cosx)/cosx] / [ (sinx + cosx)/(sinxcosx)]
= (sinx+ cosx)/cosx * (sinxcosx)/(sinx+cosx)
= sinxcosx/cosx
= sinx
= RS