I need help proving these 2 identities.
1. If x = 18 degrees, prove that sin2x = cos3x. Find the exact values of sinx and cosx
2. If 2sin(x - y) = sin(x + y), prove that tanx = 3tan y
Please help!
I can't think of a way to help you on the first part, but for finding the exact value of sine and cosine:
<-- Divide both sides by cos(x)
Using the quadratic formula:
Note that both solutions are acceptable, indicating that there are actually 4 solutions for x in . Obviously the sin(18) will correspond to the positive solution.
From the sine equation we can find cosine:
where the indicates which quadrant the angle is in. (So for 18 degrees, pick + because cosine is positive in the first quadrant.)
-Dan