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

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

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2cos(x)=sin(x)

2 cos (x) = sin (x)

x = 1.10714 \dots + πn

Degrees

x = 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

2 cos (x) = sin (x)

Rewrite using trig identities

2 cos (x) = sin (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

2 = tan (x)

Switch sides

tan (x) = 2

tan (x) = 2

Apply trig inverse properties

tan (x) = 2

General solutions for

tan (x) = 2

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

x = arctan (2) + πn

x = arctan (2) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn

cot (\frac{3 θ}{2}) = - 3

sin^{2} (2 x) - sin (2 x) - 2 = 0

tan^{2} (x) - 3 sec (x) = - 3

2 sin (\frac{1}{2} x) - 2 = 0

11 sin (b) - 1 = 3 sin (b) - 1

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