Question

sin a /X = cos a /y prove that sin a - cos a = x-y/√x²+y²​

Answer 1

Answer:

Differentiate each side wrt x we get

cosy dy/dx = cos (a+y) - xsin(a+y) dy/dx

Replace x from original equation, rearrange dy/dx,

dy/dx (cosy + sin(a+y) siny/cos(a+y)) = cos(a+y)

Multiply both sides by cos(a+y)

dy/dx (cosycos(a+y) +sinysin(a+y)) =(cos(a+y))^2

dy/dx(cos(a+y-y)) =(cos(a+y)) ^2

So, dy/dx = cos^2(a+y)/cosa

Hence proved