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

The general solution for 3+sin(x)=3cos^2(x) is x=2pin,x=pi+2pin,x=-0.33983…+2pin,x=pi+0.33983…+2pin

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

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

x = 2 πn, x = π + 2 πn, x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn

Solution steps

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

Subtract

3 cos^{2} (x)

from both sides

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

Rewrite using trig identities

sin (x) + 3 sin^{2} (x) = 0

Solve by substitution

sin (x) = 0, sin (x) = - \frac{1}{3}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

Combine all the solutions

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

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn

cot (θ) = 3

sin^{2} (x) + 4 sin (x) = 0

(tan (x) - 1) (sec (x) - 1) = 0

4 - 8 sin^{2} (x) = 0

1 - sin (θ) = 3 cos (θ)

What is the general solution for 3+sin(x)=3cos^2(x) ?
The general solution for 3+sin(x)=3cos^2(x) is x=2pin,x=pi+2pin,x=-0.33983…+2pin,x=pi+0.33983…+2pin