Q. 154.5( 4 Votes )

# If <i

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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