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

The general solution for 2cos^2(x)=sin(2x) is x= pi/2+2pin,x=(3pi)/2+2pin,x= pi/4+pin

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2cos^2(x)=sin(2x)

2 cos^{2} (x) = sin (2 x)

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{4} + πn

Solution steps

2 cos^{2} (x) = sin (2 x)

Subtract

sin (2 x)

from both sides

2 cos^{2} (x) - sin (2 x) = 0

Rewrite using trig identities

2 cos^{2} (x) - 2 cos (x) sin (x) = 0

Factor

2 cos^{2} (x) - 2 cos (x) sin (x) : 2 cos (x) (cos (x) - sin (x))

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

Solving each part separately

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

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

cos (x) - sin (x) = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{4} + πn

tan (θ) + cot (θ) = 4 sin (2 θ)

2 cos^{2} (θ) - 7 cos (θ) + 3 = 0

sin (x) = 0, 0 \leq x \leq 2 π

tan (x) sin (x) - 4 tan (x) = - 3 tan (x)

7 tan (x) sin (x) - 2 sin (x) = 0

What is the general solution for 2cos^2(x)=sin(2x) ?
The general solution for 2cos^2(x)=sin(2x) is x= pi/2+2pin,x=(3pi)/2+2pin,x= pi/4+pin