What is the general solution for (sin(x)-1)(cos(x)-1/2)=0 ?

The general solution for (sin(x)-1)(cos(x)-1/2)=0 is x= pi/2+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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(sin(x)-1)(cos(x)-1/2)=0

(sin (x) - 1) (cos (x) - \frac{1}{2}) = 0

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

Solution steps

(sin (x) - 1) (cos (x) - \frac{1}{2}) = 0

Solving each part separately

sin (x) - 1 = 0 or cos (x) - \frac{1}{2} = 0

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

cos (x) - \frac{1}{2} = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

2 sin^{4} (x) = 4 - 7 cos^{2} (x)

4 cos^{2} (A) - 1 = 0

sin (\frac{75 π}{11}) = sin (\frac{x π}{11})

sec^{2} (θ) = \frac{4}{3}

cos (x) = \frac{5}{3}

What is the general solution for (sin(x)-1)(cos(x)-1/2)=0 ?
The general solution for (sin(x)-1)(cos(x)-1/2)=0 is x= pi/2+2pin,x= pi/3+2pin,x=(5pi)/3+2pin