if (a+b)tan(theta-phi) = (a-b)tan(theta + phi) and a cos2 phi + b cos2 theta =c then prove that a square - b square + c square = 2 ac cos2 phi.

my soln.

a+b/a-b = tan(t + p)/tan(t-p)

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- Aug 28th 2011, 10:47 AM #1

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- Aug 28th 2011, 10:58 AM #2

- Aug 28th 2011, 06:56 PM #3

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- Aug 29th 2011, 01:43 PM #4
## Re: tan and cos

In the first equation, write the tans as sin/cos and then use the trig formulas for sums and products, to get

You also have the equation , from which

Square the equations (1) and (2) and add:

That simplifies to give the result that you want.

Notice that this is really a problem about a triangle, with sides a, b, c and angles (opposite the side a) and (opposite the side b). The equation (1) is then the sine rule, and the equation is the cosine rule.