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

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

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sin(2t)=-cos(2t)

sin (2 t) = - cos (2 t)

t = \frac{3 π}{8} + \frac{πn}{2}

Solution steps

sin (2 t) = - cos (2 t)

Rewrite using trig identities

tan (2 t) = - 1

General solutions for

tan (2 t) = - 1

2 t = \frac{3 π}{4} + πn

Solve

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

t = \frac{3 π}{8} + \frac{πn}{2}

cos (3 θ) = sin (3 θ)

cos (5 x) = 1, 0 \leq x \leq \frac{π}{2}

sec (x) = - 1 + tan (x)

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

x, csc (x) + cot (x) = 1

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