Question

What is the value of tan(9) - tan(27) - tan(63) + tan(81)? (all in degrees)

This is on a non-calculator paper. Thanks in advance for the answer.

Answer 1

`4`

Explanation:

`x=tan81+tan9-(tan63+tan27)`

=`cot9+tan9-(cot27+tan27)`

=`[(cos9)^2+(sin9)^2]/(sin9*cos9)-[(cos27)^2+(sin27)^2]/(sin27*cos27)`

=`1/(sin9*cos9)-1/(sin27*cos27)`

=`2/sin18-2/sin54`

=`2*(sin54-sin18)/(sin54*sin18)`

=`(4cos36*sin18)/(cos36*sin18)`

=`4`