If $$cosec^2$$ θ = 625/576, then what is the value of [(sin θ - cos θ)/(sin θ + cos θ)]?

Given : $$cosec^2\theta=\frac{625}{576}$$

=> $$cosec\theta=\sqrt{\frac{625}{576}}=\frac{25}{24}$$

=> $$sin\theta=\frac{24}{25}$$

Using, $$sin^2\theta+cos^2\theta=1$$

=> $$cos^2\theta=1-(\frac{24}{25})^2$$

=> $$cos^2\theta=1-\frac{576}{625}=\frac{(625-576)}{625}=\frac{49}{625}$$

=> $$cos\theta=\sqrt{\frac{49}{625}}=\frac{7}{25}$$

$$\therefore$$ $$(sin\theta-cos\theta)=\frac{24}{25}-\frac{7}{25}=\frac{17}{25}$$

Similarly, $$(sin\theta+cos\theta)=\frac{24}{25}+\frac{7}{25}=\frac{31}{25}$$

To find : $$\frac{(sin\theta-cos\theta)}{(sin\theta+cos\theta)}$$

= $$\frac{17}{25}\div\frac{31}{25}$$

= $$\frac{17}{25}\times\frac{25}{31}=\frac{17}{31}$$

=> Ans - (C)