What is the general solution for sin(x-pi/2)+cos(x+pi/2)=0 ?

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

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sin(x-pi/2)+cos(x+pi/2)=0

sin (x - \frac{π}{2}) + cos (x + \frac{π}{2}) = 0

x = \frac{3 π}{4} + πn

Solution steps

sin (x - \frac{π}{2}) + cos (x + \frac{π}{2}) = 0

Rewrite using trig identities

- 1 - tan (x) = 0

Move

1

to the right side

- tan (x) = 1

Divide both sides by

- 1

tan (x) = - 1

General solutions for

tan (x) = - 1

x = \frac{3 π}{4} + πn

\frac{3}{2} = sin (arcsin (0) + c)

1 + 2 sin^{2} (x) - 3 sin (x) = 0

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

\frac{1}{2} = \frac{1}{2} \cdot cos (4.2 t + \frac{π}{6})

120 = 8 3^{2} + 7 5^{2} - 2 \cdot 83 \cdot 75 \cdot cos (x)

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