If \sin\theta + \cos\theta = \frac{7}{5}, what is \sin\theta\cos\theta?

\frac{12}{25} (\sin\theta+\cos\theta)^2=1+2\sin\theta\cos\theta=\frac{49}{25}, so 2\sin\theta\cos\theta=\frac{24}{25} and \sin\theta\cos\theta=\frac{12}{25}.

Right Triangles and Trigonometry

SAT Math· difficulty 4/5

\sin\theta + \cos\theta = \frac{7}{5}

A
$\frac{24}{25}$
B
$\frac{7}{25}$
C
$\frac{49}{50}$
D
$\frac{12}{25}$
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Explanation

(\sin\theta+\cos\theta)^2=1+2\sin\theta\cos\theta=\frac{49}{25}

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