2sin^2 b + 4cos(a+b)sinasinb + cos2(a+b) = ??

Question

amistre64 · Answer

any other information?

anonymous · Answer

options are sin2a , cos2a, sin2b, cos2b

amistre64 · Answer

that last term cos^2 (a+b)  or  cos[2(a+b)] ??  the ascii is a bit vague since people tend to mistype exponent carrots

anonymous · Answer

cos[2(a+b)]

amistre64 · Answer

seems like a nightmare of just applying identities ..

cos(a+b) = cosa cosb - sina sinb

if a=b the its cos^2 a - sin^2 a
           or   2 cos^2 a - sin a
           or          cos a - 2sin^2 a

anonymous · Answer

so what will the answer be?

amistre64 · Answer

dunno, have to run the gambit of simplifying the given with identities

amistre64 · Answer

notice that sina sinb = cosa cosb - cos(a+b)  but this might not be useful

cos(a+b) can be replaced by cosa cosb - sina sinb which may reduce some things .... but at the moment its just a mess

anonymous · Answer

im trying it out, it just keeps getting more and more complicated.

amistre64 · Answer

cos 2(a+b) = cos(2) cos(a+b) - sin(2) sin(a+b)  which doesnt seem useful at the moment

amistre64 · Answer

yeah its a pain :)

anonymous · Answer

i got it, i guess. we can take cos2(a+b) as cos(2a+2b) right?

amistre64 · Answer

we can yes

anonymous · Answer

then, im getting cos2a

amistre64 · Answer

chk with the wolf :)

anonymous · Answer

wolf? x)

amistre64 · Answer

http://www.wolframalpha.com/input/?i=2sin%5E2%28b%29+%2B+4cos%28a%2Bb%29sin%28a%29sin%28b%29+%2B+cos%282%28a%2Bb%29%29 cos 2a seems good

anonymous · Answer

ohh. thanks. :D