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Popular >

1/2 tan(2x)=tan(x)

Solution

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

Solution

x = πn

+1

Solution steps

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

Subtract

tan (x)

from both sides

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

Simplify

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

\frac{tan ( 2 x ) - 2 tan ( x )}{2} = 0

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

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

Rewrite using trig identities

\frac{2 tan ^{3} ( x )}{1 - tan ^{2} ( x )} = 0

Solve by substitution

tan (x) = 0

tan (x) = 0 : x = πn

Combine all the solutions

x = πn

Popular Examples

sin(x+pi)+cos(x+pi)=0

sin (x + π) + cos (x + π) = 0

2sin^2(x)-3sin(x)=-1,0<= x<= 2pi

2 sin^{2} (x) - 3 sin (x) = - 1, 0 \leq x \leq 2 π

5cos(x)+2sqrt(3)=cos(x)

5 cos (x) + 23 = cos (x)

cos^2(x)+2sin(x)-2=0

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

tan^2(θ)=sqrt(3)tan(θ)

tan^{2} (θ) = 3 tan (θ)

Frequently Asked Questions (FAQ)

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