I need help on some math questions?

Question

Establish each of the following identities:
1. tanΘ secΘ (cscΘ -sinΘ )=1

2. tanΘ + cotΘ = 1/sinΘ cosΘ

and i have to solve these, but i don't know how, if anyone can show me. Thanks

Answer 1

1. tanΘ secΘ (cscΘ -sinΘ )=1
LHS = (sinΘ/cosΘ)(1/cosΘ) (1/sinΘ -sinΘ)
LHS = (sinΘ/cos^2Θ)(1-sin^Θ)/sinΘ
LHS = (sinΘ/cos^2Θ)(cos^2Θ/sinΘ) = 1

2. tanΘ + cotΘ = 1/(sinΘ cosΘ)
sinΘ/cosΘ +cosΘ/sinΘ = 1/(sinΘ cosΘ)
(Sin^2Θ +cos^2Θ)/sinΘcosΘ = 1/(sinΘ cosΘ)
1/(sinΘcosΘ) = 1/(sinΘ cosΘ)

Answer 2

tan sec( csc - sin )
= sin / cos * 1/cos * (1/sin - sin )
= 1 / cos^2 * (1 - sin^2)
= cos&2 / cos^2 = 1

tan + cot
= sin / cos + cos / sin
= (sin^2 + cos^s ) / (sin cos) =
1/(sin cos)