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

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

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

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

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

Solution steps

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

Rewrite using trig identities

2 cos (x) = 3

Divide both sides by

2

cos (x) = \frac{3}{2}

General solutions for

cos (x) = \frac{3}{2}

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

4 sin^{2} (θ) = 2

sinh (x) = \frac{33}{56}

2 sin (x) = cos (2 x) + 2

tan (x) = \frac{7}{12}

cos (x) = 1 - sin (x)

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