Q. 184.7( 4 Votes )

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Answer :

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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