If $\tan A=\frac{2}{3}$, then what is the value of the following?
$\left(5 \sin ^2 A-2 \cos ^2 A\right) \div\left(15 \sin ^2 A+3 \cos ^2 A\right)$
Answer & explanation
Correct answer: option 2
$\left(5 \sin ^2 A-2 \cos ^2 A\right) \div\left(15 \sin ^2 A+3 \cos ^2 A\right)$
Dividing denominator and numerator by cos²A
= $\frac{5\frac{sin^2A}{cos^2A}-2}{15\frac{sin^2A}{cos^2A}+3}$
= $\frac{5tan^2A - 2}{15tan^2A +3}$
Putting the value of tanA
= $\frac{5.\frac{4}{9} - 2}{15.\frac{4}{9} + 3}$
= $\frac{\frac{2}{9}}{\frac{29}{3}}$
= $\frac{2}{87}$