If cos^-1 x/2 + cos^-1 y/3 = a, then prove that 9x^2 - 12xy cos a + 4y^2 = 36 sin^2a.

Question

If cos^-1\(\frac x2\) + cos^-1 \(\frac y3\) = a, then prove that 9x² - 12xy cos a + 4y² = 36 sin²a.

Answer 1

Given:-  cos^-1\(\frac x2\) + cos^-1 \(\frac y3\) = a

Take

 cos^-1\(\frac x2\) + cos^-1 \(\frac y3\) = a

We know that, Formula

Hence Proved