2 questions about proving identities with sec x, cosec x, cot x

Question

I tried several things, but I just don't know how to prove them, nothing worked. Please help me with a detailed way to solve this, please add even the smallest manipulations, I'd be so grateful! 

A) sec x + tan x ≡ cos x / (1 - sin x) 

B) 1 - 2cos²x ≡ sin²x - cos²x

 

 

Answer 1

A) sec+tan=cos/(1-sin)

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

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

if you cross multiply you will see that the two sides are equal

however...

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

1-sin^2/(1-sin)(cos)=cos/((1-sin)

sin^2+cos^2=1

cos^2/(1-sin)(cos)=cos/(1-sin)

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

 

 

B)

1-2cos^2=sin^2-cos^2

1-cos^2-cos^2=sin^2-cos^2

(1-cos^2)-cos^2=sin^2-cos^2

sin^2-cos^2=sin^2-cos^2