Question

Value of Tan 15°????

Answer 1

Let  tan(15°) = tan(45°-30°) We know that tan(A - B) = (tanA - tanB) /(1 + tan A tan B)⇒tan(45°-30°) = (tan45°- tan30°)/(1+tan45°tan30°) = {1- (1/√3)} / {1+(1/√3)} ∴ tan15° = (√3 - 1) / (√3 + 1)

Answer 2

Answer:

tan (15°) = 2 - √3

Step-by-step explanation:

Tan (30° ) = tan (2*15°)

1/√3  = 2 tan (15°) / (1- tan ²(15°))

√3 = (1- tan ²(15°) / 2 tan (15°)

tan ²(15°) + 2√3 tan (15°) -1 =0

tan (15°) = -2√3 + √ (2√3)² -4 (1)(-1) / 2(1)

= -2√3±√16 / 2

= -√3±2

So,

tan (15°) = 2 - √3 or - (2 + √3)

As, tan 15° falls in the first quadrant, tan (15°) > 0

Therefore,

tan (15°) = 2 - √3

On simplification we get, 0.26794919243.