Answer:
[tex]sin(a)=cos(b)[/tex]
Step-by-step explanation:
we know that
In the triangle abc
if [tex]m\angle a+m\angle b=90^o[/tex]
then
[tex]m\angle c=90^o[/tex]
Because, the sum of the interior angles in a triangle must be equal to 180 degrees
therefore
Triangle abc is a right triangle
see the attached figure to better understand the problem
The sine of angle a is equal to divide the opposite side to angle a by the hypotenuse
so
[tex]sin(a)=\frac{x}{z}[/tex]
The cosine of angle b is equal to divide the adjacent side to angle b by the hypotenuse
so
[tex]cos(b)=\frac{x}{z}[/tex]
therefore
[tex]sin(a)=cos(b)[/tex]
When two angles are complementary, the sine of one angle is equal to the cosine of the other angle and the cosine of one angle is equal to the sine of the other angle
so
[tex]sin(a)=cos(b)[/tex]
[tex]cos(a)=sin(b)[/tex]
