Question

If cos (
$\alpha$
+
$\beta$
) = 0.5, then find sin (
$\alpha$
+
$\beta$
).

​

Answer 1

Step-by-step explanation:

$\cos( \alpha + \beta ) = 0.5 \\ \\ we \: \: take \: ( \alpha + \beta ) = x \\ \\ so \: \\ \cos(x) = 0.5 \\ \\ { \cos(x) }^{2} + { \sin(x) }^{2} = 1 \\ {0.5}^{2} + { \sin(x) }^{2} = 1 \\ { \sin(x) }^{2} = 1 - 0.25 \\ { \sin(x) }^{2} = 0.75 \\ \sin(x) = \sqrt{0.75} \\ \\ \sin( \alpha + \beta ) = \sqrt{0.75}$