What is the general solution for cos^2(x)=3sin(x)cos(x) ?

The general solution for cos^2(x)=3sin(x)cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=0.32175…+pin

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cos^2(x)=3sin(x)cos(x)

cos^{2} (x) = 3 sin (x) cos (x)

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 0.32175 \dots + πn

Solution steps

cos^{2} (x) = 3 sin (x) cos (x)

Subtract

3 sin (x) cos (x)

from both sides

cos^{2} (x) - 3 sin (x) cos (x) = 0

Factor

cos^{2} (x) - 3 sin (x) cos (x) : cos (x) (cos (x) - 3 sin (x))

cos (x) (cos (x) - 3 sin (x)) = 0

Solving each part separately

cos (x) = 0 or cos (x) - 3 sin (x) = 0

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

cos (x) - 3 sin (x) = 0 : x = arctan (\frac{1}{3}) + πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = arctan (\frac{1}{3}) + πn

Show solutions in decimal form

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 0.32175 \dots + πn

cos (θ) - 3 cos (2 θ) = 0

sin^{2} (x) + 3 sin (x) = 4

sin (y) = \frac{50}{65.3}

0.26 = \frac{1 - sin ( x )}{1 + sin ( x )}

sec (x) = - 2, 0 \leq x \leq 2 π

What is the general solution for cos^2(x)=3sin(x)cos(x) ?
The general solution for cos^2(x)=3sin(x)cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=0.32175…+pin