Question

if sin alpha = 4/5 find the value of sin 2alpha

Answer 1

this is your answer

Answer 2

Hey!!
We know,

${ \cos}^{2} \alpha = 1 - { \sin }^{2} \alpha \\ \ { \cos}^{2} \alpha = 1 - ( \frac{4}{5} )^{2} \\ \cos \alpha = \frac{3}{5} .$
Agin, We know,
$\sin(2 \alpha ) = 2 \sin\alpha \ .\cos \alpha \\ \sin(2 \alpha ) = 2 \times \frac{4}{5} \times \frac{3}{5} \\ so \: \: \sin(2 \alpha ) = \frac{24}{25} ..$
::::::Thank you::::