What is the general solution for 4sin^2(x)=1 ?

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

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4sin^2(x)=1

4 sin^{2} (x) = 1

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

Solution steps

4 sin^{2} (x) = 1

Solve by substitution

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

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

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

Combine all the solutions

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

cot (- \frac{5 π}{6})

sec (3 x) = 2

cos (2 θ) + 6 sin^{2} (θ) = 4

sin (\frac{5 π}{6})

cos (- \frac{3 π}{2})

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