verifying trigonometric identities

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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

  • verifying trigonometric identities -

    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 ;)

  • verifying trigonometric identities -

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

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