# Choose the correc

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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