If $$\sec \theta +\tan \theta=2$$, then the value of $$\sin \theta$$ is:

Given : $$\sec \theta +\tan \theta=2$$ -----------(i)

Also, $$sec^2\theta-tan^2\theta=1$$

=> $$(sec\theta-tan\theta)(sec\theta+tan\theta)=1$$

=> $$\sec \theta -\tan \theta=\frac{1}{2}$$ ----------(ii)

Adding equations (i) and (ii), => $$2sec\theta=2+\frac{1}{2}=\frac{5}{2}$$

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

=> $$cos\theta=\frac{4}{5}$$

$$\therefore$$ $$sin\theta=\sqrt{1-cos^2\theta}$$

= $$\sqrt{1-(\frac{4}{5})^2}=\sqrt{1-\frac{16}{25}}$$

= $$\sqrt{\frac{9}{25}}=\frac{3}{5}$$

=> Ans - (D)