What is the general solution for sin((3pi)/2-2x)=sin(x) ?

The general solution for sin((3pi)/2-2x)=sin(x) is x= pi/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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sin((3pi)/2-2x)=sin(x)

sin (\frac{3 π}{2} - 2 x) = sin (x)

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

Solution steps

sin (\frac{3 π}{2} - 2 x) = sin (x)

Rewrite using trig identities

- cos (2 x) = sin (x)

Subtract

sin (x)

from both sides

- cos (2 x) - sin (x) = 0

Rewrite using trig identities

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

Solve by substitution

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

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

α, sin (α) - sin (β) = cos (β) - cos (α)

- \frac{6}{7} = tan (t)

sin (2 x) = 3

sin (3 x) cos (2 x) = 0

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

What is the general solution for sin((3pi)/2-2x)=sin(x) ?
The general solution for sin((3pi)/2-2x)=sin(x) is x= pi/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin