Question

How do I do these problems?
Verify the identity.
a= alpha, b=beta, t= theta

1. (1 + sin a) (1 - sin a)= cos^2a
2. cos^2b - sin^2b = 2cos^2b - 1
3. sin^2a - sin^4a = cos^2a - cos^4a
4. (csc^2 t / cot t) = csc t sec t
5. (cot^2 t / csc t) = csc t = sin t

Answer 1

Learn your identites well in order to prove these.
1. (1+sina) (1-sina)
= 1-sina+sina-sin^2a
= 1-sin^2a
= cos^2a (according to identity)

2. cos^2b-sin^2b
you know that sin^2b = 1-cos^2b, so:
cos^2b-(1-cos^2b)
=cos^2b-1+cos^2b
=2cos^2b-1

3. sin^2a - sin^4a=
= sin^2a- (sin^2a)(sin^2a)
=(1-cos^2a)-(1-cos^2a)(1-cos^2a)
=1-cos^2a- (1-2cos^2a+cos^4a)
=1-cos^2a-1+2cos^2a-cos^4a
=cos^2a-cos^4a

I hope you can do the rest by yourself ;)

Answer 2

1-sin^2B
------------- = csc^2B-sec^2B
sin^2Bcos^2B