The trigonometric expression is
.
Let
and
, then
and
.
Draw one right triangle with an acute angle
and another with an acute angle
.
Label the sides such that
and
.
Then use the Pythagorean theorem to express the length of each third side.
\
From the diagarm :
\Trigonometric ratio :
.
and
.
.
Apply tangent difference identity :
.

Substitute the values
and
.

Therefore,
.
.