# Find <span lang="

Let

Convert into sin x and cos x

Let sin x = t

As sin2x + cos2x = 1

cos2x = 1 - sin2x

Substitute in I

Using partial fractions

Canceling (1 + t)

Equating numerators

A (1 + t)(1 – t) + B(1 – t) + C(1 + t)2 = t …(a)

Now we will put different values of t in (a) to find values of A, B and C

Put t = -1 in (a)

B = -1/2

Put t = 1 in (a)

4C = 1

C = 1/4

Put t = 0 in (a)

A + (-1/2) + 1/4 = 0

A = 1/2 - 1/4

A = 1/4

Put values of A, B and C in (i)

Substitute value of in I

Resubstitute t = sin x

Hence

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