What is the general solution for sin(x+pi/4)-sin(x-pi/4)=1 ?

The general solution for sin(x+pi/4)-sin(x-pi/4)=1 is x= pi/4+2pin,x=(7pi)/4+2pin

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sin(x+pi/4)-sin(x-pi/4)=1

sin (x + \frac{π}{4}) - sin (x - \frac{π}{4}) = 1

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

Solution steps

sin (x + \frac{π}{4}) - sin (x - \frac{π}{4}) = 1

Rewrite using trig identities

2 cos (x) = 1

Divide both sides by

2

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

General solutions for

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

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

2 cos^{3} (x) = 2 cos (x)

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

cot (\frac{2 θ}{3}) = - 3

- 3 sin (2 θ) = 5 cos (2 θ), 0^{\circ} \leq 2 θ < 72 0^{\circ}

sin (4 x) = 1

What is the general solution for sin(x+pi/4)-sin(x-pi/4)=1 ?
The general solution for sin(x+pi/4)-sin(x-pi/4)=1 is x= pi/4+2pin,x=(7pi)/4+2pin