If $\sin heta + \cos heta = 1$, then $\sin heta \cdot \cos heta$ e…

Question

If $\sin	heta + \cos	heta = 1$, then $\sin	heta \cdot \cos	heta$ equals:

Accepted Answer

C. $0$

Square both sides of $\sin	heta + \cos	heta = 1$:
$(\sin	heta + \cos	heta)^2 = 1^2$
$\sin^2	heta + 2\sin	heta\cos	heta + \cos^2	heta = 1$
Using $\sin^2 + \cos^2 = 1$:
$1 + 2\sin	heta\cos	heta = 1$
$\sin	heta \cos	heta = 0$.
Verify: the original equation holds only when $	heta = 0°$ (so $\sin = 0$, $\cos = 1$) or $	heta = 90°$ (so $\sin = 1$, $\cos = 0$). In both cases the product is 0. ✓

Answer

$\dfrac{1}{2}$

Answer

$1$

Answer

$-1$

If $\sin\theta + \cos\theta = 1$, then $\sin\theta \cdot \cos\theta$ equals: