What is the general solution for tan(2x)=(((300))/(200-(-400))*2) ?

The general solution for tan(2x)=(((300))/(200-(-400))*2) is x= pi/8+(pin)/2

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tan(2x)=(((300))/(200-(-400))*2)

tan (2 x) = (\frac{( 300 )}{200 - ( - 400 )} \cdot 2)

x = \frac{π}{8} + \frac{πn}{2}

Radians

x = \frac{π}{8} + \frac{π}{2} n

Solution steps

tan (2 x) = (\frac{( 300 )}{200 - ( - 400 )} \cdot 2)

Simplify

\frac{300}{200 - ( - 400 )} \cdot 2 : 1

\frac{300}{200 - ( - 400 )} \cdot 2

Apply rule

- (- a) = a

= \frac{300}{200 + 400} \cdot 2

\frac{300}{200 + 400} = \frac{1}{2}

\frac{300}{200 + 400}

Add the numbers:

200 + 400 = 600

= \frac{300}{600}

Cancel the common factor:

300

= \frac{1}{2}

= 2 \cdot \frac{1}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

General solutions for

tan (2 x) = 1

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

2 x = \frac{π}{4} + πn

2 x = \frac{π}{4} + πn

Solve

2 x = \frac{π}{4} + πn : x = \frac{π}{8} + \frac{πn}{2}

2 x = \frac{π}{4} + πn

Divide both sides by

2

2 x = \frac{π}{4} + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{π}{4}}{2} + \frac{πn}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{π}{4}}{2} + \frac{πn}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{π}{4}}{2} + \frac{πn}{2} : \frac{π}{8} + \frac{πn}{2}

\frac{\frac{π}{4}}{2} + \frac{πn}{2}

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{π}{8}

= \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

cos (2 x) = 0.37

15 cot^{2} (x) = 5

cos (2 x) - sin (x) = 1, 0 \leq x < 2 π

sec^{2} (x) + 5 sec (x) - 14 = 0

3 cos^{2} (x) = 1

What is the general solution for tan(2x)=(((300))/(200-(-400))*2) ?
The general solution for tan(2x)=(((300))/(200-(-400))*2) is x= pi/8+(pin)/2