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

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

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

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

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

Degrees

x = 31.71747 \dots^{\circ} + 9 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

cos (2 x), cos (2 x) \neq = 0

\frac{2 cos ( 2 x )}{cos ( 2 x )} = \frac{sin ( 2 x )}{cos ( 2 x )}

Simplify

2 = \frac{sin ( 2 x )}{cos ( 2 x )}

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

2 = tan (2 x)

Switch sides

tan (2 x) = 2

tan (2 x) = 2

Apply trig inverse properties

tan (2 x) = 2

General solutions for

tan (2 x) = 2

tan (x) = a \Rightarrow x = arctan (a) + πn

2 x = arctan (2) + πn

2 x = arctan (2) + πn

Solve

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

2 x = arctan (2) + πn

Divide both sides by

2

2 x = arctan (2) + πn

Divide both sides by

2

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

Simplify

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

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}

0.322 = sin (3.92232 \cdot t)

cos (x) tan^{2} (x) = 3 cos (x), 0 \leq x < 2 π

2 - cos (2 x) + 1 = 0

cos (2 x) = \frac{3}{4}

sin (x) = 0.7, 0^{\circ} \leq x \leq 36 0^{\circ}

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