In this question, sin-1(4/5) + sin-1(5/13) + sin-1(16/65) = pi/2 Instead of solving it straight away, I took the sin-1(16/65) term to the right hand side and thus proved that sin-1(4/5) + sin-1(5/13) = cos-1(16/65). Is it correct to do so? Will I be awarded marks if in case this question happens to appear in the exam? Share with your friends Share 30 Manbar Singh answered this We have to prove, sin-145 + sin-1513 + sin-11665 = π2⇒sin-145 + sin-1513 = π2 - sin-11665⇒sin-145 + sin-1513 = cos-11665We will just prove sin-145 + sin-1513 = cos-11665LHS = sin-145 + sin-1513Let sin-145 = x and sin-1513 = y⇒sin x = 45 and sin y = 513Now, cos x = 1-sin2x = 1 - 1625 = 35Now, cos y = 1-sin2y = 1 - 25169 = 1213Now, cosx+y = cos x . cos y - sin x . sin y⇒cosx+y = 35 × 1213 - 45×513⇒cosx+y =3665 - 2065⇒cosx+y = 1665⇒x + y = cos-11665⇒sin-145 + sin-1513 = cos-11665 39 View Full Answer Thamarai Selvi answered this ya. its right!! 4