What is the general solution for sin(x+pi/2)+sin(x-(3pi)/2)=1 ?

The general solution for sin(x+pi/2)+sin(x-(3pi)/2)=1 is x=2pin+pi/2+(7pi)/6 ,x=2pin+pi/2+(11pi)/6

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sin(x+pi/2)+sin(x-(3pi)/2)=1

sin (x + \frac{π}{2}) + sin (x - \frac{3 π}{2}) = 1

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

Solution steps

sin (x + \frac{π}{2}) + sin (x - \frac{3 π}{2}) = 1

Rewrite using trig identities

- 2 sin (\frac{2 x - π}{2}) = 1

Divide both sides by

- 2

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

General solutions for

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

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

Solve

\frac{2 x - π}{2} = \frac{7 π}{6} + 2 πn : x = 2 πn + \frac{π}{2} + \frac{7 π}{6}

Solve

\frac{2 x - π}{2} = \frac{11 π}{6} + 2 πn : x = 2 πn + \frac{π}{2} + \frac{11 π}{6}

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

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

cos (θ) = - \frac{2}{3}

8 tan (x) sin (x) = 7 sin (x)

cos (x) = 2 cos (x) - 1

sin^{3} (x) + cos^{3} (x) = 0

What is the general solution for sin(x+pi/2)+sin(x-(3pi)/2)=1 ?
The general solution for sin(x+pi/2)+sin(x-(3pi)/2)=1 is x=2pin+pi/2+(7pi)/6 ,x=2pin+pi/2+(11pi)/6