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

The general solution for sin(x)*cos(x)=2cos^2(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=1.10714…+pin

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

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

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 1.10714 \dots + πn

Solution steps

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

Subtract

2 cos^{2} (x)

from both sides

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

Factor

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

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

Solving each part separately

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

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

sin (x) - 2 cos (x) = 0 : x = arctan (2) + πn

Combine all the solutions

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

Show solutions in decimal form

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 1.10714 \dots + πn

cos (θ) tan (θ) + cot (θ) = csc (θ)

tan^{2} (x) = \frac{1}{cot ( x )}

\frac{sin ( θ )}{cos ( θ )} = 3

48 sin^{2} (x) = 48 - 24 cos (x)

1 - 4 cos (2 x) = 0

What is the general solution for sin(x)*cos(x)=2cos^2(x) ?
The general solution for sin(x)*cos(x)=2cos^2(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=1.10714…+pin