Question

If tan27°=k express the following in terms of k

1.Sin27°
2.Sin63°
3.tan(-27°)

Answer 1

Answer:

Consider tan3θ−tanθ=

cos3θ

sin3θ

−

cosθ

sinθ

=

cos3θcosθ

sin2θ

=2

cos3θ

sinθ

Similarly, tan9θ−tan3θ=2

cos9θ

sin3θ

and tan27θ−tan9θ=2

cos27θ

sin9θ

∴

cos3θ

sinθ

+

cos9θ

sin3θ

+

cos27θ

sin9θ

=

2

1

(tan27θ−tanθ)

⇒k

2

=

2

1

k

1

⇒k

1

=2k

2

⇒

k

2

k

1

=2

(1)

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