Question

WRITE IN SIMPLEST FORM : COS INVERSE( 3/5 COS X + 4/5 SIN X )

Answer 1

\[p = \cos^{-1} \left( \frac{3}{5} \cos x + \frac{4}{5}\sin x \right)\]\[\cos p = \frac{3}{5} \cos x + \frac{4}{5} \sin x\]\[\cos p = \sin q \cos x + \cos q \sin x\]\[\cos p = \sin \left( q + x \right)\]\[\cos p = \cos \left( \frac{\pi}{2} - \left( q + x \right)\right)\]\[p = \frac{\pi}{2} - \left( q + x \right)\]\[p = \frac{\pi}{2} - \left( \cos^{-1} \frac{4}{5} + x \right)\]