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

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

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2cos^2(X)=1-sin(X)

2 cos^{2} (X) = 1 - sin (X)

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

Solution steps

2 cos^{2} (X) = 1 - sin (X)

Subtract

1 - sin (X)

from both sides

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

y, x = cot (y) + tan (x)

sin (θ) - 0.2 cos (θ) = \frac{8.54}{9.8}

cos (w π) = 0

2 tan (x) + sec^{2} (x) = 0, - 9 0^{\circ} < x < 9 0^{\circ}

tan (6 0^{\circ} - θ) = \frac{1}{3}

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