Hi! Can someone help me with these? I'm suppose to verify each idenity. Thanks!

Question

1.) 1/tanθ +tanθ=sec^2θ/tanθ

2.) secθ-1/1-cosθ=secθ

Answer 1

1.
LS = 1/tanØ + tanØ
= (1+tan^2 Ø)/tanØ
but 1+tan^2 Ø = sec^2 Ø, one of the basic identities in your repertoire
= sec^2 Ø/tanØ
= RS

2. for this one you must realize that secØcosØ = 1

LS = (secØ - 1)/(1 - cosØ) , those brackets are essential
= (secØ - 1)/(1 - cosØ) * (1+cosØ)/(1+cosØ)
= (secØ + secØcosØ - 1 - cosØ)/(1 - cos^2 Ø)
= (1/cosØ - cosØ)/sin^2 Ø
= ( (1 - cos^2 Ø)/cosØ )/(sin^2 Ø
= ( sin^2 Ø/cosØ)/sin^2 Ø
= 1/cosØ
= secØ
= RS