How do you solve (sec^2x-1)/(sinx)=tanxsecx?

Question

Thisis a trigonometry identity problem. 

Answer 1

(sec²x-1)/(sinx)=tanxsecx

sec²x=1+tan²x

substitute

(1+tan²x-1)/(sinx)

tan²x/sinx

tanxtanx/sinx

tanx=sinx/cosx

substitute for only one of the tanx

(sinx/cosx)(tanx)/(sinx)

(sinxtanx)/(sinxcosx)

tanx/cosx

(tanx)(1/cosx)

tanxsecx (sec=1/cos)