Q18 of 29 Page 1

Find

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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