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Trig Identities

prove that:
(sin2x +sin2y) / (cos2x + cos2y) = tan(x + y)

iv tried starting with both (sin2x +sin2y) / (cos2x + cos2y) and tan(x+y) and converting and i cant do it.

Thanks

Reply 1

steve10

Use the identities,

Unparseable latex formula:

\sin A + \sin B = 2\sin$\frac{A+B}{2}$\cdot \cos$\frac{A-B}{2}$

Unparseable latex formula:

\cos A + \cos B = 2\cos$\frac{A+B}{2}$\cdot \cos$\frac{A-B}{2}$

it falls out. :smile:

Reply 2

Jordan7

Yep cheers iv done that. Now the next part of the question says hence show that tan52.5 = root6 - root3 - root2 + 2

How do i do this? Im know i have to assign X and Y to some angle so which angles shld i use, then which formula shd i put thm into, the original one?
thanks

Reply 3

steve10

When you see something like √2 or √3 when angles are being talked about, then think about the angles 30°, 45° and 60°.

cos 30° = sin 60° = √3/2
sin 45° = cos 45° = 1/√2

Oh, and √6 = √3*√2.

So, now play around with the original identity that you had and some of those angles and see if you can come up with the solution :smile:

Reply 4

Jordan7

yh i no about all the surds etc its just 52.5 would mean u would have to hava fraction in front of one of the angles eg:

tan(x+y) 52.5 => tan[30 + 1/2(45)] so x is 30 y is 1/2(45)
... nevermind iv seen what to do cheers