Additional & Duplication Formula

[Endorser]

Hello,

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 learned 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

 

[verty]

I think the best thing is to show, as completely as you can, your best attempt to simplify that first expression, along with your thoughts on what steps you took, why you took them, where you think it is going wrong.