Question

Double-Angle and Half-Angle Identiies [See Attachment] Question 4

Answer 1

Please make it brainleist

Answer 2

We have

$\sin 2 \theta = 2 \sin \theta \cos \theta$

We already know $\sin \theta$ so we have to find $\cos \theta$.

Theta is in the first quadrant so we choose the positive sign:

$\cos \theta = \sqrt{1 - (2/5)^2} = \sqrt{21/25} = \frac 1 5\sqrt{21}$

$\sin 2 \theta = 2 (\frac 2 5)(\frac 1 5 \sqrt{21}) = \dfrac{4 \sqrt{21}}{25}$

Choice c