MCQ
If $\cos\theta=\frac{4}{5}$ then $\tan\theta=?$
- ✓$\frac{3}{4}$
- B$\frac{4}{3}$
- C$\frac{3}{5}$
- D$\frac{5}{3}$
✓
Answer
Correct option: A.
$\frac{3}{4}$
$\sin^2\theta+\cos^2\theta=1$
$\Rightarrow\sin^2\theta+\Big(\frac{4}5{}\Big)^2=1$
$\Rightarrow\sin^2\theta=1-\frac{16}{25}=\frac{9}{25}$
$\Rightarrow\sin\theta=\frac{3}{5}$
$\therefore\tan\theta=\frac{\sin\theta}{\cos\theta}$
$=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{4}$
$\Rightarrow\sin^2\theta+\Big(\frac{4}5{}\Big)^2=1$
$\Rightarrow\sin^2\theta=1-\frac{16}{25}=\frac{9}{25}$
$\Rightarrow\sin\theta=\frac{3}{5}$
$\therefore\tan\theta=\frac{\sin\theta}{\cos\theta}$
$=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{4}$
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