What is the general solution for tan(x-10)cot(20-x)=1 ?

The general solution for tan(x-10)cot(20-x)=1 is x=180n+15,x=105+180n

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tan(x-10)cot(20-x)=1

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

x = 18 0^{\circ} n + 1 5^{\circ}, x = 10 5^{\circ} + 18 0^{\circ} n

Solution steps

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

Subtract

1

from both sides

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

Simplify

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

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

Express with sin, cos

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

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

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

Rewrite using trig identities

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

General solutions for

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

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

Solve

\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 0 + 36 0^{\circ} n : x = 18 0^{\circ} n + 1 5^{\circ}

Solve

\frac{- 18 0 ^{\circ} + 18 x}{18} - \frac{18 0 ^{\circ} - 9 x}{9} = 18 0^{\circ} + 36 0^{\circ} n : x = 10 5^{\circ} + 18 0^{\circ} n

x = 18 0^{\circ} n + 1 5^{\circ}, x = 10 5^{\circ} + 18 0^{\circ} n

3 csc (2 x) - 4 sin (2 x) = 0

3 tan (B) - 4 = tan (B) - 2

sin (2 x) = 5 cos (2 x)

5 sec (2 x) + 2 = 0

2.1 sin (θ) = 1.33 sin (θ + 9 0^{\circ})

What is the general solution for tan(x-10)cot(20-x)=1 ?
The general solution for tan(x-10)cot(20-x)=1 is x=180n+15,x=105+180n