What is the general solution for sin(x+pi/4)+sin(x-pi/4)-1=0 ?

The general solution for sin(x+pi/4)+sin(x-pi/4)-1=0 is x= pi/4+2pin,x=(3pi)/4+2pin

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sin(x+pi/4)+sin(x-pi/4)-1=0

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) - 1 = 0

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

Solution steps

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) - 1 = 0

Rewrite using trig identities

- 1 + 2 sin (x) = 0

Move

1

to the right side

2 sin (x) = 1

Divide both sides by

2

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

General solutions for

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

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

\frac{1}{2} sin (x) = - \frac{3}{4}

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

7 sin (x) = cos (x) - 3

sin (a) = \frac{3}{4}

sin (7 x) + sin (x) = 0, 0 \leq x \leq 2 π

What is the general solution for sin(x+pi/4)+sin(x-pi/4)-1=0 ?
The general solution for sin(x+pi/4)+sin(x-pi/4)-1=0 is x= pi/4+2pin,x=(3pi)/4+2pin