What is the general solution for (1+(tan^2(a))/1+cot^2(a))=tan^2(a) ?

The general solution for (1+(tan^2(a))/1+cot^2(a))=tan^2(a) is No Solution for a\in\mathbb{R}

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(1+(tan^2(a))/1+cot^2(a))=tan^2(a)

(1 + \frac{tan ^{2} ( a )}{1} + cot^{2} (a)) = tan^{2} (a)

No Solution for a \in R

Solution steps

(1 + \frac{tan ^{2} ( a )}{1} + cot^{2} (a)) = tan^{2} (a)

Subtract

tan^{2} (a)

from both sides

cot^{2} (a) + 1 = 0

Solve by substitution

cot^{2} (a) + 1 = 0

Let:

cot (a) = u

u^{2} + 1 = 0

u^{2} + 1 = 0 : u = i, u = - i

u^{2} + 1 = 0

Move

1

to the right side

u^{2} + 1 = 0

Subtract

1

from both sides

u^{2} + 1 - 1 = 0 - 1

Simplify

u^{2} = - 1

u^{2} = - 1

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = - 1, u = - - 1

Simplify

- 1 : i

- 1

Apply imaginary number rule:

- 1 = i

= i

Simplify

- - 1 : - i

- - 1

Apply imaginary number rule:

- 1 = i

= - i

u = i, u = - i

Substitute back

u = cot (a)

cot (a) = i, cot (a) = - i

cot (a) = i, cot (a) = - i

cot (a) = i :

No Solution

cot (a) = i

No Solution

cot (a) = - i :

No Solution

cot (a) = - i

No Solution

Combine all the solutions

No Solution for a \in R

2 cos (x) + 1 = sin^{2} (x)

4 cos^{2} (x) - 11 cos (x) + 7 = 0

3 tan (x) + 2 sec (x) = 1

cos (a) = 0.14

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

What is the general solution for (1+(tan^2(a))/1+cot^2(a))=tan^2(a) ?
The general solution for (1+(tan^2(a))/1+cot^2(a))=tan^2(a) is No Solution for a\in\mathbb{R}