Question

How do you find the exact value of the expression `(tan25^circ+tan110^circ)/(1-tan25^circtan110^circ)`?

Answer 1

`(tan25^@+tan110^@)/(1-tan25^@tan110^@)=-1`

Explanation:

We can use the identity `(tanA+tanB)/(1-tanAtanB)=tan(A+B)`

Hence, `(tan25^@+tan110^@)/(1-tan25^@tan110^@)`

= `tan(25^@+110^@)`

= `tan135^@=tan(180^@-45^@)`

and as `tan(180^@-A)=-tanA`

`(tan25^@+tan110^@)/(1-tan25^@tan110^@)=-tan45^@=-1`