MCQ
$\left(\frac{1-\tan ^2 30^{\circ}}{1+\tan ^2 30^{\circ}}\right)$ is equal to:
- A$\sin 60^{\circ}$
- B$\tan 60^{\circ}$
- C$\cos 30^{\circ}$
- ✓$\cos 60^{\circ}$
✓
Answer
Correct option: D.
$\cos 60^{\circ}$
$\frac{1-\tan ^2 30^{\circ}}{1+\tan ^2 30^{\circ}}=\frac{1-\left(\frac{1}{\sqrt{3}}\right)^2}{1+\left(\frac{1}{\sqrt{3}}\right)^2}$
$=\frac{1-\frac{1}{3}}{1+\frac{1}{3}}$
$=\frac{\frac{2}{3}}{\frac{4}{3}}$
$=\frac{1}{2}$
$=\cos 60^{\circ}$
$=\frac{1-\frac{1}{3}}{1+\frac{1}{3}}$
$=\frac{\frac{2}{3}}{\frac{4}{3}}$
$=\frac{1}{2}$
$=\cos 60^{\circ}$
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