2ta15/1-tan^2 15

Question

Evaluate using double angle concept

2tan15/1-tan^2 15

Answer 1

Tan2A=2tanA/(1-tan^2(A)).

If A=15, tan30=2tan15/(1-tan^2(15))=1/sqrt(3) or sqrt(3)/3=0.5774.

Answer 2

2tan15°/(1-tan^2 15°)

There is a trig identity for the double angle of tangent: tan(2A) = 2tanA / (1 - tan²A)

Let A = 15°:

tan(2∙15°) = 2tan15° / (1 - tan²15°)

tan 30° = 2tan15° / (1 - tan²15°)

√3/3 = 2tan15° / (1 - tan²15°)

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