Question

How do you write the expression as the sine, cosine, or tangent of the angle given `(tan68^circ-tan115^circ)/(1+tan68^circtan115^circ)`?

Answer 1

`(tan68^@-tan115^@)/(1+tan68^@tan115^@)=-tan47^@`

Explanation:

This comes from the well known formula for finding tangent ratio of difference of two angles i.e.

`tan(A-B)=(tanA-tanB)/(1+tanAtanB)`

As such `(tan68^@-tan115^@)/(1+tan68^@tan115^@)`

= `tan(68^@-115^@)`

= `tan(-47^@)`

and as `tan(-theta)=-tantheta`, this is equal to `-tan47^@`