What is the general solution for tan(x)=tan(2x-30) ?

The general solution for tan(x)=tan(2x-30) is x=-2pin+30,x=-pi+30-2pin

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tan(x)=tan(2x-30)

tan (x) = tan (2 x - 30)

x = - 2 πn + 30, x = - π + 30 - 2 πn

Solution steps

tan (x) = tan (2 x - 30)

Subtract

tan (2 x - 30)

from both sides

tan (x) - tan (2 x - 30) = 0

Express with sin, cos

\frac{cos ( - 30 + 2 x ) sin ( x ) - cos ( x ) sin ( - 30 + 2 x )}{cos ( - 30 + 2 x ) cos ( x )} = 0

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

cos (- 30 + 2 x) sin (x) - cos (x) sin (- 30 + 2 x) = 0

Rewrite using trig identities

sin (x - (- 30 + 2 x)) = 0

General solutions for

sin (x - (- 30 + 2 x)) = 0

x - (- 30 + 2 x) = 0 + 2 πn, x - (- 30 + 2 x) = π + 2 πn

Solve

x - (- 30 + 2 x) = 0 + 2 πn : x = - 2 πn + 30

Solve

x - (- 30 + 2 x) = π + 2 πn : x = - π + 30 - 2 πn

x = - 2 πn + 30, x = - π + 30 - 2 πn

2 sin (\frac{x}{2} + \frac{π}{6}) = 1, x < 4 π, 0

16 cos^{2} (x) - 9 = 0

cos (θ) = 0.476

sin (x) = \frac{15}{19}

12 cos (x) + 6 sin (2 x) = 0, 0 \leq x \leq 2 π

What is the general solution for tan(x)=tan(2x-30) ?
The general solution for tan(x)=tan(2x-30) is x=-2pin+30,x=-pi+30-2pin