What is the general solution for 4cos^2(A)-1=0 ?

The general solution for 4cos^2(A)-1=0 is A= pi/3+2pin,A=(5pi)/3+2pin,A=(2pi)/3+2pin,A=(4pi)/3+2pin

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4cos^2(A)-1=0

4 cos^{2} (A) - 1 = 0

A = \frac{π}{3} + 2 πn, A = \frac{5 π}{3} + 2 πn, A = \frac{2 π}{3} + 2 πn, A = \frac{4 π}{3} + 2 πn

Solution steps

4 cos^{2} (A) - 1 = 0

Solve by substitution

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

cos (A) = \frac{1}{2} : A = \frac{π}{3} + 2 πn, A = \frac{5 π}{3} + 2 πn

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

Combine all the solutions

A = \frac{π}{3} + 2 πn, A = \frac{5 π}{3} + 2 πn, A = \frac{2 π}{3} + 2 πn, A = \frac{4 π}{3} + 2 πn

sin (\frac{75 π}{11}) = sin (\frac{x π}{11})

sec^{2} (θ) = \frac{4}{3}

cos (x) = \frac{5}{3}

1 + cos (x) = 1

csc (x) sec (x) = tan (x)

What is the general solution for 4cos^2(A)-1=0 ?
The general solution for 4cos^2(A)-1=0 is A= pi/3+2pin,A=(5pi)/3+2pin,A=(2pi)/3+2pin,A=(4pi)/3+2pin