Question

100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!

Answer 1

Step-by-step explanation:

to prove that both sides of the equation are equals we have to use this formula:

`\sin(a \: ± \: b) = \sin(a).\cos(b) ± \: \cos(a).\sin(b)`

hence;

`\sin(θ \: - (\pi)/(2) ) = \sin(θ) .cos( (\pi)/(2) ) - \cos(θ). \sin( (\pi)/(2) )`

now sin (π/2) = 1 and cos (π/2) = 0, therefore:

`\sin(θ- (\pi)/(2) ) = 0 -cos(θ) \\ \sin( θ- (\pi)/(2)) = - cos(θ)`