If tan A = 2/3 , then what is the value of the following? (5 sin² A - 2 cos²A) ÷(15sin²A + 3cos²A)

If tan A = 2/3 , then what is the value of the following?…

If tan A = $\frac{2}{3}$ , then what is the value of the following?

$(5 sin^2 A - 2 cos^2A) \div(15sin^2A + 3cos^2A)$

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. $\frac{2}{87}$ .

Calculations:

tan A = 2/3

sin A/cos A = 2/3

Using the values of sin A and Cos A, we get

⇒ $(5 sin^2 A - 2 cos^2A) \div(15sin^2A + 3cos^2A)$

⇒ (5 × 4 - 2 × 9) ÷ (60 + 27)

= 2/87