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

The general solution for 2sin(2x)=-cos(2x) is x=-(0.46364…)/2+(pin)/2

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

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

x = - \frac{0.46364 \dots}{2} + \frac{πn}{2}

Solution steps

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

Rewrite using trig identities

2 tan (2 x) = - 1

Divide both sides by

2

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

Apply trig inverse properties

2 x = arctan (- \frac{1}{2}) + πn

Solve

2 x = arctan (- \frac{1}{2}) + πn : x = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = - \frac{0.46364 \dots}{2} + \frac{πn}{2}

cos (2 x) + cos (\frac{π}{2} - 2 x) = - 2

cos^{2} (x) = - 1.5

2 arctan (\frac{1}{2}) - arctan (x) = \frac{π}{4}

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

sin (θ) = \frac{13}{85}

What is the general solution for 2sin(2x)=-cos(2x) ?
The general solution for 2sin(2x)=-cos(2x) is x=-(0.46364…)/2+(pin)/2