What is the general solution for 6sin^2(x)=3 ?

The general solution for 6sin^2(x)=3 is x= pi/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin,x=(7pi)/4+2pin

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6sin^2(x)=3

6 sin^{2} (x) = 3

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

6 sin^{2} (x) = 3

Solve by substitution

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

sin (x) = \frac{1}{2} : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

sin (x) = - \frac{1}{2} : x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combine all the solutions

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

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

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

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

arctan (2 x) + arctan (x) = \frac{π}{2}

sec (\frac{b}{4}) csc (\frac{b}{4}) = 2 csc (\frac{b}{4})

What is the general solution for 6sin^2(x)=3 ?
The general solution for 6sin^2(x)=3 is x= pi/4+2pin,x=(3pi)/4+2pin,x=(5pi)/4+2pin,x=(7pi)/4+2pin