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

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

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

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

No Solution for o \in R

Solution steps

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

Subtract

1

from both sides

\frac{cot ^{2} ( o ) + tan ^{2} ( o ) + 3}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )} - 1 = 0

Simplify

\frac{cot ^{2} ( o ) + tan ^{2} ( o ) + 3}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )} - 1 : \frac{- cot ^{2} ( o ) - tan ^{2} ( o ) cot ^{2} ( o ) + 1}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )}

\frac{- cot ^{2} ( o ) - tan ^{2} ( o ) cot ^{2} ( o ) + 1}{( tan ^{2} ( o ) + 2 ) ( cot ^{2} ( o ) + 1 )} = 0

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

- cot^{2} (o) - tan^{2} (o) cot^{2} (o) + 1 = 0

Rewrite using trig identities

- cot^{2} (o) = 0

Divide both sides by

- 1

cot (o) = 0

General solutions for

cot (o) = 0

o = \frac{π}{2} + πn

Since the equation is undefined for:

\frac{π}{2} + πn

No Solution for o \in R

9 (2 sin^{2} (x) - 1) = 0

sin (x) + sin^{2} (x) + sin^{3} (x) + sin^{4} (x) = 0

sin (9 x) - cos (x) = 0

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

t, 0.08 = 0.1 cos (4 t)

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