What is the general solution for (cot(x))(tan(x)-1)=0 ?

The general solution for (cot(x))(tan(x)-1)=0 is x= pi/4+pin

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(cot(x))(tan(x)-1)=0

(cot (x)) (tan (x) - 1) = 0

x = \frac{π}{4} + πn

Degrees

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

Solution steps

(cot (x)) (tan (x) - 1) = 0

Solving each part separately

cot (x) = 0 or tan (x) - 1 = 0

cot (x) = 0 : x = \frac{π}{2} + πn

cot (x) = 0

General solutions for

cot (x) = 0

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

tan (x) - 1 = 0

Move

1

to the right side

tan (x) - 1 = 0

Add

1

to both sides

tan (x) - 1 + 1 = 0 + 1

Simplify

tan (x) = 1

tan (x) = 1

General solutions for

tan (x) = 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{π}{2} + πn, x = \frac{π}{4} + πn

Since the equation is undefined for:

\frac{π}{2} + πn

x = \frac{π}{4} + πn

10 tan (θ) sec (θ) = 10 cot (θ) csc (θ)

arctan (x) = \frac{( 2 \cdot 1.8 )}{[ ( 3170 + 1.7 ) - 1 ]}

cos (4 x) + sin (\frac{x}{2}) = 0

2 sin^{2} (θ) - 5 sin (θ) = 3

cos (3 x - \frac{π}{4}) = \frac{1}{2}, 0 \leq x \leq π

What is the general solution for (cot(x))(tan(x)-1)=0 ?
The general solution for (cot(x))(tan(x)-1)=0 is x= pi/4+pin