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

The general solution for sin(2x)-cos(2x)=0 is x= pi/8+(pin)/2

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sin(2x)-cos(2x)=0

sin (2 x) - cos (2 x) = 0

x = \frac{π}{8} + \frac{πn}{2}

Solution steps

sin (2 x) - cos (2 x) = 0

Rewrite using trig identities

tan (2 x) - 1 = 0

Move

1

to the right side

tan (2 x) = 1

General solutions for

tan (2 x) = 1

2 x = \frac{π}{4} + πn

Solve

2 x = \frac{π}{4} + πn : x = \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

tan (x) - 3 cot (x) = 0

sin (\frac{θ}{2}) = - \frac{1}{2}

cos (2 x) + sin (x) = 1

cos (x + \frac{3 π}{4}) - cos (x - \frac{3 π}{4}) = 1

tan (2 θ) + 2 cos (θ) = 0

What is the general solution for sin(2x)-cos(2x)=0 ?
The general solution for sin(2x)-cos(2x)=0 is x= pi/8+(pin)/2