Help with establishing the trig identity

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. ;)
 
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