The directions are write the expression as the sine, coine, or tangent of an angle.
(tan 25 degrees + tan 10 degrees) / [1 - [(tan 25 degrees)(tan 10 degrees)]]
Hint: use the following trigonometric identity
tan(a+b)=(tan(a)+tan(b))/(1-tan(a)tan(b))
To write the expression as the sine, cosine, or tangent of an angle, we can make use of the trigonometric identity for tangent addition:
tan(A + B) = (tan A + tan B) / [1 - (tan A)(tan B)]
Here, we can see that the given expression is the same as the tangent addition formula, where A = 25 degrees and B = 10 degrees. So we can rewrite the expression using this identity:
(tan 25 degrees + tan 10 degrees) / [1 - [(tan 25 degrees)(tan 10 degrees)]]
= tan(25 degrees + 10 degrees)
= tan(35 degrees)
Therefore, the given expression can be written as the tangent of an angle, where that angle is 35 degrees.