# If <img wid

Given:

To Prove:

Let x = sinA and y = sinB ---- (i)

Putting the value in the equation we get,

Now putting the values of A and B from (i),

sin-1x – sin-1y = 2cot-1a

Now differentiating with respect to x we get,

[Proved]

OR

Given: x = a(cos2θ + 2θsin2θ) and y = a(sin2θ – 2θcos2θ)

To Find: at θ =

Differentiating x with respect to θ we get,

-- (i)

Differentiating y with respect to θ we get,

From the above two equations we get,

Differentiating with respect to x we get,

[Putting the value of from (i)]

At θ = ,

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