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

The general solution for sin(x)+sin(pi/2-x)=0 is x=(3pi)/4+2pin,x=(7pi)/4+2pin

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

sin (x) + sin (\frac{π}{2} - x) = 0

x = \frac{3 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

sin (x) + sin (\frac{π}{2} - x) = 0

Rewrite using trig identities

2 cos (\frac{4 x - π}{4}) = 0

Divide both sides by

2

cos (\frac{4 x - π}{4}) = 0

General solutions for

cos (\frac{4 x - π}{4}) = 0

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

Solve

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

Solve

\frac{4 x - π}{4} = \frac{3 π}{2} + 2 πn : x = \frac{7 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

(- \frac{1}{4}) + cos^{2} (x) = 1

x, e^{s i n (x)} = e^{- s i n (x)}

\frac{cos ( x )}{sin ( x )} = tan (x)

sin (B) = \frac{7 sin ( 3 6 ^{\circ} )}{12}

x, cos^{2} (x) = sin (y + \frac{π}{2})

What is the general solution for sin(x)+sin(pi/2-x)=0 ?
The general solution for sin(x)+sin(pi/2-x)=0 is x=(3pi)/4+2pin,x=(7pi)/4+2pin