Does anyone know how to solve number 11? I have the formulas under the question?

Question

asked Jul 14, 2020 159k views

1 Answer

Rho Phi · Answer 1 · 2020-07-20T02:11:43+0000

$\sin \alpha ( \csc \alpha - \sin \alpha )$

but

$\csc\alpha = (1)/( \sin \alpha )$

now substituting it in the formula

$\sin \alpha ( (1)/( \sin \alpha ) - \sin \alpha )$

now multiplying with the sine alpha throughout the equation

$= ( \sin \alpha )/( \sin \alpha ) - {sin}^(2) \alpha$

$= 1 - {sin}^(2) \alpha$

but mathematically

$1 - {sin}^(2) \alpha = {cos}^(2) \alpha$

hence proved.