What is the general solution for (2sin(x)cos(x))/(cos(x))=1 ?

The general solution for (2sin(x)cos(x))/(cos(x))=1 is x= pi/6+2pin,x=(5pi)/6+2pin

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(2sin(x)cos(x))/(cos(x))=1

\frac{2 sin ( x ) cos ( x )}{cos ( x )} = 1

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Degrees

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

\frac{2 sin ( x ) cos ( x )}{cos ( x )} = 1

Simplify

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

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

Cancel the common factor:

cos (x)

= 2 sin (x)

2 sin (x) = 1

Divide both sides by

2

2 sin (x) = 1

Divide both sides by

2

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

Simplify

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

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

General solutions for

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

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

csc (3 θ) = sec (1 5^{\circ})

2 cot^{2} (x) + tan (x) = cot (x)

sin (2 x) = sin (\frac{π}{2} - x)

tan (X) = 1

2 sec^{2} (x) - sec (x) - 1 = 0

What is the general solution for (2sin(x)cos(x))/(cos(x))=1 ?
The general solution for (2sin(x)cos(x))/(cos(x))=1 is x= pi/6+2pin,x=(5pi)/6+2pin