What is the general solution for (8cos(θ)-4)(5sin(θ)-5)=0 ?

The general solution for (8cos(θ)-4)(5sin(θ)-5)=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ= pi/2+2pin

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(8cos(θ)-4)(5sin(θ)-5)=0

(8 cos (θ) - 4) (5 sin (θ) - 5) = 0

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn, θ = \frac{π}{2} + 2 πn

Solution steps

(8 cos (θ) - 4) (5 sin (θ) - 5) = 0

Solving each part separately

8 cos (θ) - 4 = 0 or 5 sin (θ) - 5 = 0

8 cos (θ) - 4 = 0 : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

5 sin (θ) - 5 = 0 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn, θ = \frac{π}{2} + 2 πn

arctan (x) = \frac{π}{3}

2 cos (2 x) - 2 sin (x) = 0

cos (2 x) + 3 cos (x) - 1 = 0

cos (2 θ) = - 1

2 sin^{2} (x) - 1 = sin (x)

What is the general solution for (8cos(θ)-4)(5sin(θ)-5)=0 ?
The general solution for (8cos(θ)-4)(5sin(θ)-5)=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ= pi/2+2pin