Question

If $\sec^{2}\theta+\tan^{2}\theta=7, 0<\theta<\frac{\pi}{2}$, then $\tan 2\theta$ is equal to

• A. 1
• B. $\sqrt{3}$
• C. $\sqrt{2}$
• D. $-\sqrt{3}$
• E. 0

Hint:

Logic Tip: Alternatively, since $\tan\theta = \sqrt{3}$ in the first quadrant, $\theta$ must be exactly $60^{\circ}$ ($\frac{\pi}{3}$). Therefore, $\tan 2\theta = \tan(120^{\circ}) = -\sqrt{3}$. Finding the angle directly is often faster than using the formula.

Answer 1

The Correct Option is D