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

The general solution for sin(x)+2(cos(x))^2=1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/2+2pin

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

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

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

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

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

a sin (2 θ) = 0

cos (2 x) = 0, x \leq 2 π, 0

7 + csc (2 x) = 3 cot^{2} (2 x)

cos (θ) = cos (\frac{π}{13})

sin (2 x + \frac{π}{6}) = - 1

What is the general solution for sin(x)+2(cos(x))^2=1 ?
The general solution for sin(x)+2(cos(x))^2=1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/2+2pin