Answer:
cosβ
Step-by-step explanation:
cot(β+π)sinβ
cot(x)=cos(x)/sin(x), so we can rewrite our expression as:
(cos(β+π)/sin(β+π)) * sinβ
sin(a+b)=sin(a)cos(b)+cos(a)sin(b), so we can rewrite our expression as:
(cos(β+π)/(sinβcosπ+cosβsinπ)) * sin(β)
cos(a+b)=cos(a)cos(b)-sin(a)sin(b), so we can rewrite our expression as:
(cosβcosπ-sinβsinπ)/(sinβcosπ+cosβsinπ)) * sin(β)
cosπ=-1 and sinπ=0, so we can rewrite our expression as:
(-cosβ)/(-sinβ) * sin(β)
(-cosβ)/(-sinβ) * sin(β)
=(cosβ/sinβ)(sinβ)
=cosβ
