If sin A = 5/13 , then find the value of (cosA-2tanA)/(sinA +3tanA) .

If sin A = 5/13 , then find the value of…

If sin A = $\frac{5} {13}$ , then find the value of $\frac{cosA-2tanA}{sinA +3tanA}$ .

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. $\frac{14}{255}$ .

sin A = 5/13

⇒ sin²A = (5/13)² = 25/169

⇒ cos²A = 1 - sin²A = 1 - (25/169) = 144/169

⇒ cos A = √(144/169) = 12/13

⇒ tan A = sin A/cos A = (5/13)/(12/13) = 5/12

Now, (cos A - 2tan A)/(sin A + 3tan A)

= [12/13 - 2(5/12)]/[5/13 + 3(5/12)]

= (12/13 - 10/12)/(5/13 + 15/12)

= (7/78)/(85/52)

= 14/255

Therefore, the value of the expression is 14/255.