If =4 5 then =? - Vidyadip

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.

$\frac{3}{4}$

$\sin^2\theta+\cos^2\theta=1$
$\Rightarrow\sin^2\theta+\Big(\frac{4}5{}\Big)^2=1$
$\Rightarrow\sin^2\theta=1-\frac{16}{25}=\frac{9}{25}$
$\Rightarrow\sin\theta=\frac{3}{5}$
$\therefore\tan\theta=\frac{\sin\theta}{\cos\theta}$
$=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{4}$

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