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

The general solution for sin(2x)=2cos(2x) is x=(1.10714…)/2+(pin)/2

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

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

x = \frac{1.10714 \dots}{2} + \frac{πn}{2}

Solution steps

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

Rewrite using trig identities

tan (2 x) = 2

Apply trig inverse properties

2 x = arctan (2) + πn

Solve

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

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

Show solutions in decimal form

x = \frac{1.10714 \dots}{2} + \frac{πn}{2}

5 tan^{2} (x) - 7 = 8

3 sin (2 y) - 4 sin (2 y) cos (2 y) = 0

sin (x) + sin (4 x) = 0

cos (0.568 x - 2.595) = 0

8 tan (- x + \frac{π}{8}) = 8

What is the general solution for sin(2x)=2cos(2x) ?
The general solution for sin(2x)=2cos(2x) is x=(1.10714…)/2+(pin)/2