What is the general solution for tan(2θ)=(2tan(θ))/(1-tan(θ)) ?

The general solution for tan(2θ)=(2tan(θ))/(1-tan(θ)) is θ=pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(2θ)=(2tan(θ))/(1-tan(θ))

tan (2 θ) = \frac{2 tan ( θ )}{1 - tan ( θ )}

θ = πn

Solution steps

tan (2 θ) = \frac{2 tan ( θ )}{1 - tan ( θ )}

Subtract

\frac{2 tan ( θ )}{1 - tan ( θ )}

from both sides

tan (2 θ) - \frac{2 tan ( θ )}{1 - tan ( θ )} = 0

Simplify

tan (2 θ) - \frac{2 tan ( θ )}{1 - tan ( θ )} : \frac{tan ( 2 θ ) ( 1 - tan ( θ ) ) - 2 tan ( θ )}{1 - tan ( θ )}

\frac{tan ( 2 θ ) ( 1 - tan ( θ ) ) - 2 tan ( θ )}{1 - tan ( θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

tan (2 θ) (1 - tan (θ)) - 2 tan (θ) = 0

Rewrite using trig identities

- \frac{2 tan ^{2} ( θ )}{1 + tan ( θ )} = 0

Solve by substitution

tan (θ) = 0

tan (θ) = 0 : θ = πn

Combine all the solutions

θ = πn

sec (θ) = 15, tan (2 θ) + 125 (cos (2 θ) - 1)

2 cos (θ) + 1 = 0

\frac{1}{1 - sin ( x )} = 2 sec^{2} (x) + tan (x) sec (x)

42 tan (x) - 2 = 32 tan (x)

7 sin (2 x) + 12 cos (x) = 0

What is the general solution for tan(2θ)=(2tan(θ))/(1-tan(θ)) ?
The general solution for tan(2θ)=(2tan(θ))/(1-tan(θ)) is θ=pin