Q19 of 354 Page 12

Differentiate the following functions with respect to x:


Let x = cos2θ


Now



Using 1 – 2sin2θ = cos2θ and 2cos2θ – 1 = cos2θ



Now




Using sin(A + B) = sinA cosB + cosA sinB



Considering the limits,


0 < x < 1


0 < cos 2θ < 1




Now,





Differentiating w.r.t x, we get





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