I don't understand how to solve these, can you help?

Question

Verify each identity

(a)

tanΘ + secΘ = cos Θ/1-sinΘ

(b)

tan²Θ - sin²Θ = sin²Θ tan²Θ

Answer 1

I'm going to leave out Θ to make it easier to write.

tan+sec=cos/(1-sin)

(sin/cos)+(1/cos)=(cos)/(1-sin)

(sin+1)/(cos)=(cos)/(1-sin) cross multiply or multiply both sides by (cos)(1-sin) to get...

(sin+1)(1-sin)=(cos)(cos)

(1+sin)(1-sin)=(cos)(cos)

1-sin^2=cos^2

1=sin^2+cos^2 (true trig identity)

tan^2-sin^2=sin^2tan^2

(sin^2/cos^2)-sin^2=sin^2tan^2

(sin^2/cos^2)-(sin^2cos^2/(cos^2)=sin^2tan^2

(sin^2-sin^2cos^2)/(cos^2)=sin^2tan^2

[(sin^2)(1-cos^2)]/(cos^2)=sin^2tan^2

[(sin^2)/(cos^2)](1-cos^2)=sin^2tan^2

tan^2sin^2=sin^2tan^2 because tan=sin/cos and sin^2+cos^2=1 which means sin^2=1-cos^2