What is the general solution for 2cos(x)+2sin(x)cos(x)=0 ?

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

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

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

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

Solution steps

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

Factor

2 cos (x) + 2 sin (x) cos (x) : 2 cos (x) (sin (x) + 1)

2 cos (x) (sin (x) + 1) = 0

Solving each part separately

cos (x) = 0 or sin (x) + 1 = 0

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

sin (x) + 1 = 0 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

100 cos (3 0^{\circ}) - 200 cos (θ) = 0

x, y = sin (2 x + 3 y)

cos (θ) = \frac{8}{9}

2 sin (x) - cos (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

8 tan (A) + 3 = 2 tan (A) + 3

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