Answer :

We need to find the value of


Let


Now, take sine on both sides,



Using the property of inverse trigonometry,


sin(sin-1 A) = A



Let us find the value of cos x.


We know by trigonometric identity, that


sin2 x + cos2 x = 1


cos2 x = 1 – sin2 x



Put the value of sin x,







We have,



…(i)


Using the trigonometric identity,


cos 2x = cos2 x – sin2 x


cos 2x = (1 – sin2x) – sin2 x [, sin2 x + cos2 x = 1]


cos 2x = 1 – sin2 x – sin2 x


cos 2x = 1 – 2 sin2 x


Or,


2 sin2 x = 1 – cos 2x




Replacing x by x/4,




Substituting the value of in equation (i),


…(ii)


Using the trigonometric identity,


cos 2x = cos2 x – sin2 x


cos 2x = cos2 x – (1 – cos2 x) [, sin2 x + cos2 x = 1]


cos 2x = cos2 x – 1 + cos2x


cos 2x = 2 cos2 x – 1


Or,


2 cos2 x = 1 + cos 2x




Replacing x by x/2,




Substituting the value of in equation (ii),



Put the value of cos x as found above, cos x = 1/8.










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