Question

Sam claims that cos X= sin y and y are congruent angels is that correct

Answer 1

the complete question in the attached figure

we know that
if x and y are complementary
then
x+y=90°-------> y=90-x
and
sin(y)=sin(90-x)
remember---------> sin(A-B)=sin A cos B - cos A sin B
sin(90-x)=sin 90 cos x - cos 90 sin x
sin(90-x)=(1)* cos x - (0)* sin x-----------> cos(x)
therefore
sin(y)=cos (x)

the answer is
the option C). No, cos X = sin Y if X and Y are complementary angles