Q15 of 26 Page 1

If , x2 ≤ 1 ,then find

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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