Help with establishing the trig identity

[KappaGoku9000]

http://gyazo.com/8c603bb53cfbca8a3ea64f7996bf1ee9
Need help with 11 and 8
http://gyazo.com/a224a1b16c8ed7c1071d618eb72a494b
And 9
I've done some other establishing identities but these really have me stumped
Please help

 

[stapel]

http://gyazo.com/8c603bb53cfbca8a3ea64f7996bf1ee9
Need help with 11 and 8
http://gyazo.com/a224a1b16c8ed7c1071d618eb72a494b
And 9
I've done some other establishing identities but these really have me stumped

To other users:

The following text is displayed at the links:

9. Establish the identity: [ sin(A) + cos(B) ]² + [ cos(B) + sin(A) ] * [ cos(B) - sin(A) ] = 2 cos(B) [ sin(A) + cos(B) ]

(no work shown)

11. Establish the identity: [ 2a sin(A) cos(A) ]² + a² [ cos²(A) - sin² (A) ]² = a²

work shown:

[ 2a sin(A) cos(A) ][ 2a sin(A) cos(A) ]. . . . .[ cos²(A) - sin² (A) ][ cos²(A) - sin² (A) ]

4a² sin²(a) cos²(A) + a² [ cos⁴(A) - sin²(A) cos²(A) - cos²(A) sin²(A) + sin²(A) ]

4a² sin²(a) cos²(A) + a² [ cos⁴(A) - 2 sin²(A) cos²(A) + sin²(A) ]

4a² sin²(a) cos²(A) + a² cos⁴(A) - 2 a² sin²(A) cos²(A) + a² sin²(A)

There is no exercise (8) in either of the postings (though there is an exercise (12) at the first link).

To the original poster:

Hint: Check your final term in the second purple line above.