If tan A = 3over4 , find the value of the following expression (6 sin A)/(1 - sin A)

If tan A = 3over4 , find the value of the following…

If tan A = $3\over4$ , find the value of the following expression
$\frac{6 \sin A}{1 - \sin A}$

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 9.

tan A = 3/4

⇒ In a right triangle, opposite = 3, adjacent = 4

⇒ Hypotenuse = √(3² + 4²) = √25 = 5

So,

sin A = 3/5

Now,

6 sin A / (1 - sin A) = 6 × (3/5) / (1 - 3/5)

= (18/5) / (2/5) = 18/5 × 5/2 = 9