Using the identities
,
you can get
.
Set and
Have a question i'm having some trouble with,
Verify the identity;
(sin A + sin 3A) / (cos A + cos 3A) = tan 2A
not sure best way to go about this one,
tried using sin3A = sin(2A + A) and expanding out but didn't seem to give me anything i wanted.
Any help would be greatly appreciated.
Cheers.
So you have
sin (a + b) = sin a cos b + sin b cos a
sin (a - b) = sin a cos b - sin b cos a
Adding the two equations gives you
sin (a + b) + sin (a - b) = 2 sin a cos b.
Now set x = a + b and y = a - b, find a and b in terms of x and y, and you'll get the identity for sin x + sin y
(similar for cos x + cos y).