Urgent to help Find theta for this equation 800sinthetacosth

Urgent to help.

Find theta for this equation.

800sin(theta)cos(theta) - 800cos(theta) + 100cos(theta) = 0.

Find theta in degrees.

Thank you.

Solution

800sin(theta)cos(theta) - 800cos(theta) + 100cos(theta) = 0

800sin()cos() - 800cos() + 100cos() = 0

800sin()cos() - 700cos() = 0

100cos()(8sin() - 7) = 0

cos()=0,(8sin() - 7) = 0

cos()=0,sin() = 7_/8

in the interval (0,2)

=_/2,3_/2 ;sin^-1(7_/8),-sin^-1(7_/8)

general solution is

=(2n+1)_/2 ,2n+sin^-1(7_/8),2n+-sin^-1(7_/8) where n is an integer