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

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

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sin^2(a)=(1-cos(a))/2

sin^{2} (a) = \frac{1 - cos ( a )}{2}

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

Solution steps

sin^{2} (a) = \frac{1 - cos ( a )}{2}

Subtract

\frac{1 - cos ( a )}{2}

from both sides

sin^{2} (a) - \frac{1 - cos ( a )}{2} = 0

Simplify

sin^{2} (a) - \frac{1 - cos ( a )}{2} : \frac{2 sin ^{2} ( a ) - 1 + cos ( a )}{2}

\frac{2 sin ^{2} ( a ) - 1 + cos ( a )}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

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

Solve by substitution

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

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

cos (a) = 1 : a = 2 πn

Combine all the solutions

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

cos (x) = \frac{- 11}{12}

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

\frac{sin ^{22} ( a )}{sin ^{2} ( a )} = 4 - 4 sin^{2} (a)

tan^{3} (x) = 2

sin^{3} (x) = 3 sin (x)

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