If $$ 7sin^2 \theta + 3cos^2\theta = 4 $$, then the value of $$ tan \theta is ( \theta $$ is acute)
Given that $$ 7sin^2 \theta + 3cos^2\theta = 4 $$
=> $$ 3sin^2 \theta + 3cos^2\theta + 4 sin^2 \theta = 4 $$
=>Â $$ 3(sin^2 \theta + cos^2\theta) + 4 sin^2 \theta = 4 $$
=>Â $$ 3 + 4 sin^2 \theta = 4 $$
=>Â $$ 4 sin^2 \theta = \frac{4}{3} $$
=>Â $$ sin^2 \theta = \frac{1}{3} $$
=> $$ sin \theta = \frac{1}{\sqrt{3}} $$
=> $$ \theta $$ = $$30^\circ $$
Therefore, $$ tan30^\circ $$ = $$ \frac{1}{\sqrt{3}}$$
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