Q. 284.5( 6 Votes )

If <img wid

Answer :

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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