If cosx = siny and cot ( x-40°) = tan (50°-y), then the value of x and y are ;

Given : $$cos x=sin y$$

=> $$sin(90^\circ-x)=siny$$

=> $$(90^\circ-x)=y$$

=> $$x+y=90^\circ$$ ---------(i)

Also, $$cot(x-40^\circ)=tan(50^\circ-y)$$

=> $$cot(x-40^\circ)=tan[90^\circ-(40^\circ+y)]$$

Using, $$tan(90^\circ-\theta)=cot \theta$$

=> $$cot(x-40^\circ)=cot(40^\circ+y)$$

=> $$x-40^\circ=40^\circ+y$$

=> $$x-y=80^\circ$$ -----------(ii)

Adding equations (i) and (ii), => $$2x=80^\circ+90^\circ=170^\circ$$

=> $$x=\frac{170^\circ}{2}=85^\circ$$

and $$y=90^\circ-85^\circ=5^\circ$$

=> Ans - (C)