What is the general solution for 5sin(x)-1=2cos^2(x) ?

The general solution for 5sin(x)-1=2cos^2(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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5sin(x)-1=2cos^2(x)

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Subtract

2 cos^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = - 3

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = - 3 :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

tan^{2} (x) + 23 tan (x) + 3 = 0

7 tan (θ) - 8 = 5 tan (θ) - 5

sin (θ) = 0.99

sin (θ) = 0.93

sin (θ) = 0.78

What is the general solution for 5sin(x)-1=2cos^2(x) ?
The general solution for 5sin(x)-1=2cos^2(x) is x= pi/6+2pin,x=(5pi)/6+2pin