Question

Sin-1 63/65 = sin-1 5/13 + cos-1 3/5

Answer 1

We have to prove that,sin−1(513) + cos−1(35) = sin−1(6365)Let sin−1(513) = x⇒sin x = 513 ⇒ cos x = 1−sin2x−−−−−−−−√ = 1213Let cos−1(35) = y⇒cos y = 35 ⇒sin y =1−cos2y−−−−−−−−√ = 45now, sin(x+y) = sin x . cos y + cos x . sin y⇒sin[sin−1(513) + cos−1(35)] = 513×35 + 1213 × 45 = 6365⇒sin−1(513) + cos−1(35) = sin−1(6365)
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