If $$\sin \theta = 4 \cos \theta$$, then what is the value of $$\sin \theta \cos \theta$$ ?
Given that,
$$\sin \theta = 4 \cos \theta$$
So,
$$\dfrac{\sin \theta}{ \cos \theta} = 4$$
$$\tan \theta = 4$$
$$\tan \theta=\dfrac{AB}{BC}=\dfrac{4}{1}$$
$$\Rightarrow AB^2+BC^2=AC^2$$
$$\Rightarrow 4^2+1= AC^2$$
$$\Rightarrow \sqrt{17} =AC$$
So
$$\sin \theta=\dfrac{AB}{AC}=\dfrac{4}{\sqrt{17}}$$
$$\cos \theta=\dfrac{BC}{AC}=\dfrac{1}{\sqrt{17}}$$
Now, substituting the values,
$$\sin \theta \cos \theta =\dfrac{4}{\sqrt{17}} \times \dfrac{1}{\sqrt{17}}=\dfrac{4}{17}$$
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