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

The general solution for sin^2(x)=3cos(x) is x=1.26319…+2pin,x=2pi-1.26319…+2pin

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

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

x = 1.26319 \dots + 2 πn, x = 2 π - 1.26319 \dots + 2 πn

Solution steps

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

Subtract

3 cos (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = - \frac{3 + 13}{2}, cos (x) = \frac{13 - 3}{2}

cos (x) = - \frac{3 + 13}{2} :

No Solution

cos (x) = \frac{13 - 3}{2} : x = arccos (\frac{13 - 3}{2}) + 2 πn, x = 2 π - arccos (\frac{13 - 3}{2}) + 2 πn

Combine all the solutions

x = arccos (\frac{13 - 3}{2}) + 2 πn, x = 2 π - arccos (\frac{13 - 3}{2}) + 2 πn

Show solutions in decimal form

x = 1.26319 \dots + 2 πn, x = 2 π - 1.26319 \dots + 2 πn

2 sin^{2} (x) + sin (x) = 1, 0 \leq x < 2 π

cos (\frac{7 π}{8} - x) = \frac{2}{2}

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

5 tan (2 x) - 5 cot (x) = 0

sec (x) = 1.742506

What is the general solution for sin^2(x)=3cos(x) ?
The general solution for sin^2(x)=3cos(x) is x=1.26319…+2pin,x=2pi-1.26319…+2pin