Trigonometry...Pls Help!!?

Question

Find the value of Tan (9) - Tan (27) - Tan (63) + Tan (81). Without using trigonometry tables...

Answer 1

Find value of Tan (9) - Tan (27) - Tan (63) + Tan (81).

= Tan (9) + Tan (81) - Tan (27) - Tan (63)

= Tan (9) + Tan (90-9) - Tan (27) - Tan (90-27)

= Tan (9) + Cot (9) - Tan (27) - Cot(27)

= Tan (9) + 1/Tan (9) - Tan (27) - 1/Tan (27)

= (Tan^2 (9) + 1)/Tan (9) - (Tan^2 (27) + 1)/Tan (27)

= Sec^2(9)/Tan (9) - Sec^2 (27) /Tan (27)

= 1/Sin (9)Cos(9) -1/Sin (27)Cos(27)

Multiply each side by 2 to nominator and denominator

= 2/2Sin (9)Cos(9) -2/2Sin (27)Cos(27)

= 2/Sin (18)) -2/Sin (54)

= 2/0.309-2/0.809

= 6.4-2.4

= 4

The value of Tan (9) - Tan (27) - Tan (63) + Tan (81) = 4.