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? 

We have to prove,    sin-145 + sin-1513 +  sin-11665 = π2sin-145 + sin-1513 = π2 - sin-11665sin-145 + sin-1513 = cos-11665We will just prove sin-145 + sin-1513 = cos-11665LHS = sin-145 + sin-1513Let sin-145 = x   and  sin-1513 = ysin 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 ycosx+y = 35 × 1213 - 45×513cosx+y =3665 - 2065cosx+y = 1665x + y = cos-11665sin-145 + sin-1513 =  cos-11665

  • 39
ya. its right!!
 
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