Question

What is the value of tan 3θ ? if tan θ = 1/2

(a) 1/5

(b) -11/2

(c) -1/5

(d) 11/2

Answer 1

Answer:

The correct answer is (d) $\frac{11}{2}$.

Step-by-step explanation:

tan θ: Law of tangent is another name for tan. The ratio of a triangle's opposite side to its adjacent side is known as the tangent formula for a right-angled triangle. The angle's sine to cosine ratio can also be used to express the angle.

Given: tan θ $= 1/2$

To find:  the value of tan 3θ.

Solution: The formula of tan 3θ is shown below.

$tan 3$θ= $3tan$θ- $tan^{3}$θ/$1-3$$tan^{2}$θ

Substitute values.

$tan 3$θ=$\frac{3*\frac{1}{2}-(\frac{1}{2})^{3}}{1-3*(\frac{1}{2})^{2}}$

$tan 3$θ=$\frac{11*4}{8*1}=\frac{11}{2}$

Calculate value of tan 3θ.

$tan3$θ=$\frac{11}{2}$

The value of tan3θ is  $\frac{11}{2}$.

(d) $11/2$ is the right answer.

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