Question

using the formula tan2theta =2tantheta/1-tansquare theta
obtain the value of tan15​

Answer 1

Answer:

2-√3

Step-by-step explanation:

θ = 15°

tan2θ=tan2(15°)=tan30°

We know that,

Tan2θ=2tanθ/(1-tan²θ)

=>Tan30°=2tan15°/(1-tan²15°)

=>1/√3 =2tan15°/(1-tan²15°)

=>1-tan²15=2√3 tan 15°

=>tan²15° + 2√3 tan15° - 1 = 0

Now, by Quadratic Formula, we have

=> Tan15°=[-2√3 ± √{(-2√3)² - 4(1)(-1)}] / 2(1)

=(-2√3+√16)/2

=(4–2√3)/2

=2-√3

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