Question

Which option equals tan 40°? Select all that apply.

Answer 1

Answers
(sin40)/(cos40)  and 
(cos50)/(sin50)

Explanations
Tangent is a trigonometric ratio given by,
tan = opposite/adjacent.
lets take,
x⇒adjacent
y⇒opposite
h⇒hypotenuse

tanФ=y/x
sinФ=y/h  and 
cosФ=x/h

(sinФ)/(cosФ) = y/h ÷ x/h
                      =y/h×h/x
                      =y/x
This shows that
(sinФ)/(cosФ) = tanФ

We also know that,
sinФ = cos(90-Ф). So,
sin40 = cos(90-40) =cos50

So therefore;

tan40 = (sin40)/(cos40) = (cos50)/(sin50)