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

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

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

sin (\frac{3 π}{2} + x) + sin (\frac{3 π}{2} + x) = - 2

x = 2 πn

Solution steps

sin (\frac{3 π}{2} + x) + sin (\frac{3 π}{2} + x) = - 2

Simplify

sin (\frac{3 π}{2} + x) + sin (\frac{3 π}{2} + x) : 2 sin (\frac{3 π}{2} + x)

2 sin (\frac{3 π}{2} + x) = - 2

Divide both sides by

2

sin (\frac{3 π}{2} + x) = - 1

General solutions for

sin (\frac{3 π}{2} + x) = - 1

\frac{3 π}{2} + x = \frac{3 π}{2} + 2 πn

Solve

\frac{3 π}{2} + x = \frac{3 π}{2} + 2 πn : x = 2 πn

x = 2 πn

cos (x) tan (x) = 0

cos^{2} (x) + 4 cos (x) + 3 = 0

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

2 sin^{2} (x) - sin (x) - 1 = 0, 0 \leq x < 2 π

sin^{2} (x) = 3

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