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

The general solution for 2sin^2(x)+cos(x)=1 is x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=2pin

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2sin^2(x)+cos(x)=1

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

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 2 πn

Solution steps

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

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 2 πn

arcsin (\frac{3}{5})

arcsin (- \frac{3}{2})

cot (x) = \frac{sin ( 2 x )}{1 - cos ( 2 x )}

tan (- \frac{5 π}{6})

tan (\frac{5 π}{8})

What is the general solution for 2sin^2(x)+cos(x)=1 ?
The general solution for 2sin^2(x)+cos(x)=1 is x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=2pin