What is the general solution for tan(x+20)*tan(x-20)=1 ?

The general solution for tan(x+20)*tan(x-20)=1 is x=45+180n,x=135+180n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(x+20)*tan(x-20)=1

tan (x + 2 0^{\circ}) \cdot tan (x - 2 0^{\circ}) = 1

x = 4 5^{\circ} + 18 0^{\circ} n, x = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

tan (x + 2 0^{\circ}) tan (x - 2 0^{\circ}) = 1

Subtract

1

from both sides

tan (x + 2 0^{\circ}) tan (x - 2 0^{\circ}) - 1 = 0

Simplify

tan (x + 2 0^{\circ}) tan (x - 2 0^{\circ}) - 1 : tan (\frac{9 x + 18 0 ^{\circ}}{9}) tan (\frac{9 x - 18 0 ^{\circ}}{9}) - 1

tan (\frac{9 x + 18 0 ^{\circ}}{9}) tan (\frac{9 x - 18 0 ^{\circ}}{9}) - 1 = 0

Express with sin, cos

\frac{- cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{18 0 ^{\circ} + 9 x}{9} ) + sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) sin ( \frac{18 0 ^{\circ} + 9 x}{9} )}{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( \frac{18 0 ^{\circ} + 9 x}{9} )} = 0

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

- cos (\frac{- 18 0 ^{\circ} + 9 x}{9}) cos (\frac{18 0 ^{\circ} + 9 x}{9}) + sin (\frac{- 18 0 ^{\circ} + 9 x}{9}) sin (\frac{18 0 ^{\circ} + 9 x}{9}) = 0

Rewrite using trig identities

- cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{18 0 ^{\circ} + 9 x}{9}) = 0

Divide both sides by

- 1

cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{18 0 ^{\circ} + 9 x}{9}) = 0

General solutions for

cos (\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{18 0 ^{\circ} + 9 x}{9}) = 0

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{18 0 ^{\circ} + 9 x}{9} = 9 0^{\circ} + 36 0^{\circ} n, \frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{18 0 ^{\circ} + 9 x}{9} = 27 0^{\circ} + 36 0^{\circ} n

Solve

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{18 0 ^{\circ} + 9 x}{9} = 9 0^{\circ} + 36 0^{\circ} n : x = 4 5^{\circ} + 18 0^{\circ} n

Solve

\frac{- 18 0 ^{\circ} + 9 x}{9} + \frac{18 0 ^{\circ} + 9 x}{9} = 27 0^{\circ} + 36 0^{\circ} n : x = 13 5^{\circ} + 18 0^{\circ} n

x = 4 5^{\circ} + 18 0^{\circ} n, x = 13 5^{\circ} + 18 0^{\circ} n

18 cos (10 x) + 2 = 10

cos (2 θ) = sin (2 θ)

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

tan (x) (cot (x) - \frac{3}{3}) = 0

24 sin^{2} (x) = 24 - 12 cos (x)

What is the general solution for tan(x+20)*tan(x-20)=1 ?
The general solution for tan(x+20)*tan(x-20)=1 is x=45+180n,x=135+180n