if  $$tan\theta =\frac{3}{5}$$ , $$0<\theta<90^\circ$$ then $$sin\theta cos\theta$$ is equal to:

Given,

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

From the triangle,

$$\text{Hypotenuse}^2=3^2+5^2$$

$$=$$>  Hypotenuse = $$\sqrt{34}$$

$$\sin\theta\ =\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{3}{\sqrt{34}}$$

$$\cos\theta\ =\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{5}{\sqrt{34}}$$

$$\therefore\ \sin\theta\ \cos\theta\ =\frac{3}{\sqrt{34}}\times\frac{5}{\sqrt{34}}=\frac{15}{34}$$

Hence, the correct answer is Option D