Question 141

If tan $$\ \theta\ $$= $$\ \frac{2}{3}\ $$, then what is the value of $$\ \frac{15sin^{2} \theta-3cos^{2} \theta}{5sin^{2} \theta+3cos^{2} \theta}$$?

Solution

Given : $$tan\ \theta=\frac{2}{3}$$

=> $$\frac{sin\ \theta}{cos\ \theta}=\frac{2}{3}$$

Let $$sin\ \theta=2$$ and $$cos\ \theta=3$$

To find : $$\ \frac{15sin^{2} \theta-3cos^{2} \theta}{5sin^{2} \theta+3cos^{2} \theta}$$

= $$\frac{15(2)^2-3(3)^2}{5(2)^2+3(3)^2}$$

= $$\frac{60-27}{20+27}$$

= $$\frac{33}{47}$$

=> Ans - (C)

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