What is the general solution for 4cos(2x)-2sin(2x)=0 ?

The general solution for 4cos(2x)-2sin(2x)=0 is x=(1.10714…)/2+(pin)/2

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4cos(2x)-2sin(2x)=0

4 cos (2 x) - 2 sin (2 x) = 0

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

Solution steps

4 cos (2 x) - 2 sin (2 x) = 0

Rewrite using trig identities

4 - 2 tan (2 x) = 0

Move

4

to the right side

- 2 tan (2 x) = - 4

Divide both sides by

- 2

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}

cos (2 x) sin (x) + sin (x) = 5 cos (2 x) + 5

3 cot (θ) = 3

sec (x) = 1, - 2 π \leq x \leq 2 π

tan (t) = \frac{4}{3}, sin (t)

cos (x) = \frac{2}{6}

What is the general solution for 4cos(2x)-2sin(2x)=0 ?
The general solution for 4cos(2x)-2sin(2x)=0 is x=(1.10714…)/2+(pin)/2