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

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

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

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

a = 2 πn, a = π + 2 πn

Solution steps

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

Solve by substitution

cos (a) = 1, cos (a) = - 1

cos (a) = 1 : a = 2 πn

cos (a) = - 1 : a = π + 2 πn

Combine all the solutions

a = 2 πn, a = π + 2 πn

tan^{2} (x) cot (x) = 1

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

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

1 + cos^{2} (a) = 3 sin (x) cos (x)

3 cos (x) + sin (x) = cos (x) - 2 sin (x)

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