if sin θ= 3/5 is equal to $$\frac{\tan\theta+\cos\theta}{\cot\theta+cosec\theta}$$ is equal to

Expression : $$sin \theta = \frac{3}{5}$$

We know that, $$cos \theta = \sqrt{1 - sin^2 \theta}$$

=> $$cos \theta = \sqrt{1 - \frac{9}{25}} = \sqrt{\frac{16}{25}}$$

=> $$cos \theta = \frac{4}{5}$$

Similarly, $$tan \theta = \frac{3}{4}$$

$$cot \theta = \frac{4}{3}$$

$$cosec \theta = \frac{5}{3}$$

To find : $$\frac{\tan \theta+\cos \theta}{\cot \theta+cosec \theta}$$

Using above values, we get :

= $$\frac{\frac{3}{4} + \frac{4}{5}}{\frac{4}{3} + \frac{5}{3}}$$

= $$\frac{\frac{31}{20}}{\frac{9}{3}}$$

= $$\frac{31}{60}$$