Answer :

As the expression for y is quite complicated. So we need to simplify it before differentiation.


For simplification we can use idea like:


1 + cos 2θ = 2cos2θ or 1 - cos 2θ = 2sin2θ


For simplifying y, put x2 = cos 2θ


y =


y =


y =


Dividing numerator and denominator by cos θ


y =


y =


y =


Now differentiating y w.r.t x, we get –



x2 = cos 2θ sin 2θ =


Differentiating the equation above w.r.t θ-




From above we have a value of sin 2θ




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