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

The general solution for sin(x)-cos(x)=0,0<= x<= 2pi is x= pi/4 ,x=(5pi)/4

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sin(x)-cos(x)=0,0<= x<= 2pi

sin (x) - cos (x) = 0, 0 \leq x \leq 2 π

x = \frac{π}{4}, x = \frac{5 π}{4}

Solution steps

sin (x) - cos (x) = 0, 0 \leq x \leq 2 π

Rewrite using trig identities

tan (x) - 1 = 0

Move

1

to the right side

tan (x) = 1

General solutions for

tan (x) = 1

x = \frac{π}{4} + πn

Solutions for the range

0 \leq x \leq 2 π

x = \frac{π}{4}, x = \frac{5 π}{4}

tan (x) + tan^{2} (x) = 0

\frac{tan ( x )}{2} = 1

sin (2 θ) + 2 sin (θ) = 0

tan (\frac{x}{2} + π) + 1 = 0

sin (x + \frac{π}{2}) = 1

What is the general solution for sin(x)-cos(x)=0,0<= x<= 2pi ?
The general solution for sin(x)-cos(x)=0,0<= x<= 2pi is x= pi/4 ,x=(5pi)/4