# Math Help - Trigonometric Proof

1. ## Trigonometric Proof

If cos x cos y = cos θ, prove that:

sin^2 (x/2) cos^2 (y/2) +cos^2 (x/2) sin^2 (y/2) = sin^2 (θ/2)

2. Originally Posted by yobacul
If cos x cos y = cos θ, prove that:

sin^2 (x/2) cos^2 (y/2) +cos^2 (x/2) sin^2 (y/2) = sin^2 (θ/2)

Hint: Start with the formula $\cos\phi = 1-2\sin^2(\phi/2)$. Apply that to all three angles $x,\,y,\,\theta$ in the formula $\cos x \cos y = cos \theta$, and see if you rearrange the result to get the desired conclusion.

3. ## Nope ...

I tried to .... I managed to get what I required on the RHS but I didn't manage to rearrange the rest to get the LHS.

4. Originally Posted by yobacul
I managed to get what I required on the RHS but I didn't manage to rearrange the rest to get the LHS.
$\cos x\cos y = \cos\theta$

$(1-2\sin^2(x/2))(1-2\sin^2(y/2)) = 1-2\sin^2(\theta/2)$

$1 - 2\sin^2(x/2) -2\sin^2(y/2) + 4\sin^2(x/2)\sin^2(y/2) = 1-2\sin^2(\theta/2)$

Subtract 1 from both sides and divide by –2:

$\sin^2(x/2) +\sin^2(y/2) -2\sin^2(x/2)\sin^2(y/2) = \sin^2(\theta/2)$

Now write the left side of that as

$\sin^2(x/2)(1 - \sin^2(y/2)) + \sin^2(y/2)(1 - \sin^2(x/2))$

and you should be able to see how to complete the calculation from there.