Consider the right triangle ABC with sides a, b, and c as shown in the figure.
Let [tex]m(\angle A)=\alpha[/tex], and [tex]m(\angle B)=\beta[/tex].
[tex]\alpha +\beta=90^{\circ}[/tex], so angles A and B are complementary.
According to the definition of sine, and cosine:
[tex]\displaystyle{ \sin \alpha= \frac{opposite\ side}{hypotenuse} =\frac{a}{c} [/tex], and
[tex]\displaystyle{ \cos \beta= \frac{adjacent\ side}{hypotenuse} =\frac{a}{c} [/tex]
Answer: they are equal.
