If = a b then =? - Vidyadip

MCQ

If $\sin\theta=\frac{\text{a}}{\text{b}}$ then $\cos\theta=?$

A
$\frac{\text{a}}{\sqrt{\text{b}^2-\text{a}^2}}$
✓
$\frac{\sqrt{\text{b}^2-\text{a}^2}}{\text{b}}$
C
$\frac{\text{a}}{\sqrt{\text{b}^2-\text{a}^2}}$
D
$\frac{\text{b}}{\text{a}}$

✓

Answer

Correct option: B.

$\frac{\sqrt{\text{b}^2-\text{a}^2}}{\text{b}}$

$\cos^2\theta=1-\sin^2\theta$
$=1-\Big(\frac{\text{a}}{\text{b}}\Big)^2$
$=1-\frac{\text{a}^2}{\text{b}^2}$
$=\frac{\text{b}^2-\text{a}^2}{\text{b}^2}$
$\Rightarrow\cos\theta=\frac{\sqrt{\text{b}^2-\text{a}^2}}{\text{b}}$

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