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

The general solution for 1+cos(a)=(2cos^2(a))/2 is a=2.23703…+2pin,a=-2.23703…+2pin

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1+cos(a)=(2cos^2(a))/2

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

a = 2.23703 \dots + 2 πn, a = - 2.23703 \dots + 2 πn

Solution steps

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

Solve by substitution

cos (a) = \frac{1 + 5}{2}, cos (a) = \frac{1 - 5}{2}

cos (a) = \frac{1 + 5}{2} :

No Solution

cos (a) = \frac{1 - 5}{2} : a = arccos (\frac{1 - 5}{2}) + 2 πn, a = - arccos (\frac{1 - 5}{2}) + 2 πn

Combine all the solutions

a = arccos (\frac{1 - 5}{2}) + 2 πn, a = - arccos (\frac{1 - 5}{2}) + 2 πn

Show solutions in decimal form

a = 2.23703 \dots + 2 πn, a = - 2.23703 \dots + 2 πn

cos (x) + cos^{4} (x) = \frac{1}{2}

sin^{2} (x) = sec (x)

5 sin^{2} (x) - 11 sin (x) + 2 = 0

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

3 sin (a) + cos (a) = 1

What is the general solution for 1+cos(a)=(2cos^2(a))/2 ?
The general solution for 1+cos(a)=(2cos^2(a))/2 is a=2.23703…+2pin,a=-2.23703…+2pin