What is the general solution for 1/((1+tan(a)))=cot(a) ?

The general solution for 1/((1+tan(a)))=cot(a) is No Solution for a\in\mathbb{R}

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1/((1+tan(a)))=cot(a)

\frac{1}{( 1 + tan ( a ) )} = cot (a)

No Solution for a \in R

Solution steps

\frac{1}{( 1 + tan ( a ) )} = cot (a)

Subtract

cot (a)

from both sides

\frac{1}{1 + tan ( a )} - cot (a) = 0

Simplify

\frac{1}{1 + tan ( a )} - cot (a) : \frac{1 - cot ( a ) ( 1 + tan ( a ) )}{1 + tan ( a )}

\frac{1 - cot ( a ) ( 1 + tan ( a ) )}{1 + tan ( a )} = 0

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

1 - cot (a) (1 + tan (a)) = 0

Rewrite using trig identities

- cot (a) = 0

Divide both sides by

- 1

cot (a) = 0

General solutions for

cot (a) = 0

a = \frac{π}{2} + πn

Since the equation is undefined for:

\frac{π}{2} + πn

No Solution for a \in R

tan (2 x) - 2 = 3 tan (x)

sin (x - \frac{π}{6}) = 0

2 = \frac{1}{cos ^{2} ( x )}

arccot (x - 2) = arccot (x - 1) + arccot (x)

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

What is the general solution for 1/((1+tan(a)))=cot(a) ?
The general solution for 1/((1+tan(a)))=cot(a) is No Solution for a\in\mathbb{R}