What is the general solution for tan(2c)=-tan(x) ?

The general solution for tan(2c)=-tan(x) is x=arctan(-tan(2c))+pin

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tan(2c)=-tan(x)

tan (2 c) = - tan (x)

x = arctan (- tan (2 c)) + πn

Solution steps

tan (2 c) = - tan (x)

Move

tan (x)

to the left side

tan (2 c) = - tan (x)

Add

tan (x)

to both sides

tan (2 c) + tan (x) = - tan (x) + tan (x)

Simplify

tan (2 c) + tan (x) = 0

tan (2 c) + tan (x) = 0

Move

tan (2 c)

to the right side

tan (2 c) + tan (x) = 0

Subtract

tan (2 c)

from both sides

tan (2 c) + tan (x) - tan (2 c) = 0 - tan (2 c)

Simplify

tan (x) = - tan (2 c)

tan (x) = - tan (2 c)

Apply trig inverse properties

tan (x) = - tan (2 c)

General solutions for

tan (x) = - tan (2 c)

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

x = arctan (- tan (2 c)) + πn

x = arctan (- tan (2 c)) + πn

2 sin (x) cos (x) = sin^{2} (x)

sin (θ) - 0.1 cos (θ) = \frac{8.87}{9.8}

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

6 sin^{2} (x) = 5 + cos (x), 18 0^{\circ} \leq x \leq 54 0^{\circ}

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

What is the general solution for tan(2c)=-tan(x) ?
The general solution for tan(2c)=-tan(x) is x=arctan(-tan(2c))+pin