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

The general solution for 4sin^2(A)-1=0 is A= pi/6+2pin,A=(5pi)/6+2pin,A=(7pi)/6+2pin,A=(11pi)/6+2pin

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4sin^2(A)-1=0

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

A = \frac{π}{6} + 2 πn, A = \frac{5 π}{6} + 2 πn, A = \frac{7 π}{6} + 2 πn, A = \frac{11 π}{6} + 2 πn

Solution steps

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

Solve by substitution

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

sin (A) = \frac{1}{2} : A = \frac{π}{6} + 2 πn, A = \frac{5 π}{6} + 2 πn

sin (A) = - \frac{1}{2} : A = \frac{7 π}{6} + 2 πn, A = \frac{11 π}{6} + 2 πn

Combine all the solutions

A = \frac{π}{6} + 2 πn, A = \frac{5 π}{6} + 2 πn, A = \frac{7 π}{6} + 2 πn, A = \frac{11 π}{6} + 2 πn

tan (θ) = \frac{22}{7}

u, x = 4 tanh (u)

tan (x) = \frac{2}{7}

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

\frac{cos ( x )}{sin ( 2 x )} = \frac{5}{7}

What is the general solution for 4sin^2(A)-1=0 ?
The general solution for 4sin^2(A)-1=0 is A= pi/6+2pin,A=(5pi)/6+2pin,A=(7pi)/6+2pin,A=(11pi)/6+2pin