Thread: 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)

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 . Apply that to all three angles in the formula , and see if you rearrange the result to get the desired conclusion.

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.

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.

Subtract 1 from both sides and divide by –2:



Now write the left side of that as



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