Question

If sin θ – cos θ = $\frac{3}{5}$, then sin θ cos θ = _______.

Answer 1

$\sin \theta -\cos \theta =\frac{3}{5}$
Squaring on both sides, we get
$$\begin{gathered} {\left(\sin \theta -\cos \theta \right)}^2={\left(\frac{3}{5}\right)}^2 \\ \Rightarrow {\sin }^2\theta +{\cos }^2\theta -2\sin \theta \cos \theta =\frac{9}{25} \\ \Rightarrow 1-2\sin \theta \cos \theta =\frac{9}{25} \\ \Rightarrow 2\sin \theta \cos \theta =1-\frac{9}{25}=\frac{16}{25} \end{gathered}$$
$\Rightarrow \sin \theta \cos \theta =\frac{8}{25}$

If sin θ – cos θ = $\frac{3}{5}$, then sin θ cos θ = $\underline{\frac{8}{25}}$.