What is the general solution for 2+cos^2(x)=5sin(x) ?

The general solution for 2+cos^2(x)=5sin(x) is x=0.57207…+2pin,x=pi-0.57207…+2pin

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2+cos^2(x)=5sin(x)

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

x = 0.57207 \dots + 2 πn, x = π - 0.57207 \dots + 2 πn

Solution steps

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

Subtract

5 sin (x)

from both sides

2 + cos^{2} (x) - 5 sin (x) = 0

Rewrite using trig identities

3 - sin^{2} (x) - 5 sin (x) = 0

Solve by substitution

sin (x) = - \frac{5 + 37}{2}, sin (x) = \frac{37 - 5}{2}

sin (x) = - \frac{5 + 37}{2} :

No Solution

sin (x) = \frac{37 - 5}{2} : x = arcsin (\frac{37 - 5}{2}) + 2 πn, x = π - arcsin (\frac{37 - 5}{2}) + 2 πn

Combine all the solutions

x = arcsin (\frac{37 - 5}{2}) + 2 πn, x = π - arcsin (\frac{37 - 5}{2}) + 2 πn

Show solutions in decimal form

x = 0.57207 \dots + 2 πn, x = π - 0.57207 \dots + 2 πn

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

cot^{5} (x) = \frac{- 1}{( 3 )}

2 cos^{4} (x) cos (x) - cos^{5} (x) = 1

cos^{4} (x) - 2 sin^{2} (x) - 1 = 0

d^{2} (1 + cos (x)) - (1 + cos (x))^{2} = sin^{2} (x)

What is the general solution for 2+cos^2(x)=5sin(x) ?
The general solution for 2+cos^2(x)=5sin(x) is x=0.57207…+2pin,x=pi-0.57207…+2pin