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I am going through some home work set to be completed before school starts and I am having trouble with a few questions.

Simplify sin(a+b)cos(a-b)-cos(a+b)sin(a-b)

Prove Identities

i. (sintheta)^2 = 1/2 -1/2cos2theta

ii. (costheta)^2 = 1/2 + 1/2cos2theta

Using what is learnt from above. find period of:

i. y=sint^2

ii. y= 1+(cos2t)^2

iii. y= 1-(4sin3t)^2

Relevant equations

cos(a+b) = cosacosb-sinasinb

cos(a-b) = cosacosb+sinasinb

sin(a+b) = sinacosb+cosasinb

sin(a-b) = sinacosb+cosasinb

sin2a=2sinacosa

cos2a = cos^2A-sin^2A

= 2cos^2A - 1

= 1-2sin^2A

cost^2 + sint^2 = 1

The attempt at a solution

I have tried numeros times to expand and simplify the equations but I never get the correct answer.

Any Help is appreciated

thanks