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

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

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

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

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

Solution steps

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

Subtract

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

from both sides

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

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

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

Rewrite using trig identities

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

Solve by substitution

cos (a) = 0, cos (a) = 1

cos (a) = 0 : a = \frac{π}{2} + 2 πn, a = \frac{3 π}{2} + 2 πn

cos (a) = 1 : a = 2 πn

Combine all the solutions

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

\frac{cot ^{2} ( x )}{2} = 3

sin (x - 3 0^{\circ}) = 0.7

\leq 3 \cdot cos (x) - sin (x) = 0

tan^{2} (x) + sec^{2} (x) = 3

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

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