Question

If $\cot \theta =\frac{24}{7}$, then $\sin \theta =$

• A. $\frac{24}{25}$
• B. $\frac{8}{25}$
• C. $\frac{7}{25}$
• D. $\frac{9}{25}$

Answer 1

Answer: (C)

$\frac{7}{25}$

Given $\cot \theta =\frac{24}{7}$

As we know that

${\text{cosec}}^2\theta =1+{\cot }^2\theta =1+(\frac{24}{7}{)}^2=(\frac{25}{7}{)}^2$

$⟹\text{cosec}\theta =\frac{25}{7}$

$⟹\sin \theta =\frac{7}{25}$