verifying trigonometric identities
posted by Anonymous on .
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

Learn your identites well in order to prove these.
1. (1+sina) (1sina)
= 1sina+sinasin^2a
= 1sin^2a
= cos^2a (according to identity)
2. cos^2bsin^2b
you know that sin^2b = 1cos^2b, so:
cos^2b(1cos^2b)
=cos^2b1+cos^2b
=2cos^2b1
3. sin^2a  sin^4a=
= sin^2a (sin^2a)(sin^2a)
=(1cos^2a)(1cos^2a)(1cos^2a)
=1cos^2a (12cos^2a+cos^4a)
=1cos^2a1+2cos^2acos^4a
=cos^2acos^4a
I hope you can do the rest by yourself ;) 
1sin^2B
 = csc^2Bsec^2B
sin^2Bcos^2B