Question 23

If $$ 7sin^2 \theta + 3cos^2\theta = 4 $$, then the value of $$ tan \theta is ( \theta $$ is acute)

Solution

Given that $$ 7sin^2 \theta + 3cos^2\theta = 4 $$

=> $$ 3sin^2 \theta + 3cos^2\theta + 4 sin^2 \theta = 4 $$

=> $$ 3(sin^2 \theta + cos^2\theta) + 4 sin^2 \theta = 4 $$

=> $$ 3 + 4 sin^2 \theta = 4 $$

=> $$ 4 sin^2 \theta = \frac{4}{3} $$

=> $$ sin^2 \theta = \frac{1}{3} $$

=> $$ sin \theta = \frac{1}{\sqrt{3}} $$

=> $$ \theta $$ = $$30^\circ $$

Therefore, $$ tan30^\circ $$ = $$ \frac{1}{\sqrt{3}}$$

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: