Question 109

If $$7 sin^{2} + 3 cos^{2} = 4$$, and θ is a positive acute angle, then tan θ is equal to

Solution

Expression : $$7 sin^{2} \theta + 3 cos^{2} \theta = 4$$

=> $$7 (1 - cos^2 \theta) + 3cos^2 \theta = 4$$

=> $$7 - 4cos^2 \theta = 4$$

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

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

$$\therefore tan \theta = \sqrt{sec^2 \theta - 1} = \sqrt{\frac{4}{3} - 1}$$

= $$\frac{1}{\sqrt{3}}$$

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