Q12 of 45 Page 1

If sin y = x sin(a + y), prove that

OR


If (cos x)y = (sin y)x, find

Given: sin y = x sin (a + y) … (1)



Differentiating both sides w. r. t to y, we get



We know that sin A cos B – cos A sin B = sin (A – B)





Hence, proved.


OR


Given: (cos x) y = (sin y) x


Taking log on both sides, we get


⇒ y log (cos x) = x log (sin y)


Differentiating w. r. to x, we get





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