Question

solve sin(1/2cos inverse4/5)

Answer 1

sin [ 1/2 * ( cos^-1 4/5 ) ] ….….. (1)

Replace cos^-1 (4/5) = β in …. (1)

So, now, REQUIRED TO FIND:

sin [ 1/2 * β ] = ?

Or, sin β/2 = ?

Since we supposed

Cos ^ -1 (4/5) = β

=> cos β = 4/5

=> cos 2 *( β/2) = 4/5

=> 1 - 2 sin² β/2 = 4/5 ( using identity)

=> 2 sin² β/2 = 1 - 4/5

=> 2 sin² β/2 = 1/5

=> sin² β/2 = 1/10

=> sin β/2 = √(1/10)

=> sin β/2 = + - ( 1/√10) ………. Ans