Question

If $\tan \theta =\frac{3}{4}$ . Find $\sin \theta ,\cos$$\theta$

Answer 1

$\tan \theta =\frac{3}{4}1+{\tan }^2\theta ={\sec }^2\theta {\sec }^2\theta =1+\frac{9}{16}{\cos }^2\theta =\frac{16}{25}\cos \theta =\pm \frac{4}{5}\cot \theta =\frac{4}{3}1+{\cot }^2\theta ={co\sec }^2\theta {\text{cosec}}^2\theta =1+\frac{16}{9}{\text{cosec}}^2\theta =\frac{25}{9}\text{cosec}\theta =\pm \frac{5}{3}\sin \theta =\pm \frac{3}{5}$