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

The general solution for sin(2x)+cos(2x)=0 is x=(3pi)/8+(pin)/2

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

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

x = \frac{3 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{3 π}{4} + πn

Solve

2 x = \frac{3 π}{4} + πn : x = \frac{3 π}{8} + \frac{πn}{2}

x = \frac{3 π}{8} + \frac{πn}{2}

sin (9 x) = - \frac{3}{2}

cos (θ) = \frac{5}{7}

2 sin (2 x) - 3 sin (x) = 0

cos (t) = - \frac{2}{2}

2 sin^{2} (3 x) = 1

What is the general solution for sin(2x)+cos(2x)=0 ?
The general solution for sin(2x)+cos(2x)=0 is x=(3pi)/8+(pin)/2