Question

cos( 2 cos-1x+sin-1x), whenx =1÷5​

Answer 1

cos-1x + sin-1x = pi/2   ............1                   (identity)

 

cos(2cos-1x+sin-1x) = cos[(cos-1x+sin-1x) + cos-1x]

=cos[pi/2 + cos-1x]                             (by using eq 1)

 

(    we know , cos[pi/2+A] = -sinA   )

 

=-sin[cos-1x]

=-sin[sin-1(1-x2)1/2]                              (cos-1x = sin-1(1-x2)1/2  )

=-(1-x2)1/2 

at x = 1/5

=-(2root6)/5