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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

((1+cot^2(x)))/(cos^2(x))=cot^2(x)

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

No Solution for x \in R

Solution steps

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

Subtract

cot^{2} (x)

from both sides

\frac{1 + cot ^{2} ( x )}{cos ^{2} ( x )} - cot^{2} (x) = 0

Simplify

\frac{1 + cot ^{2} ( x )}{cos ^{2} ( x )} - cot^{2} (x) : \frac{1 + cot ^{2} ( x ) - cot ^{2} ( x ) cos ^{2} ( x )}{cos ^{2} ( x )}

\frac{1 + cot ^{2} ( x ) - cot ^{2} ( x ) cos ^{2} ( x )}{cos ^{2} ( x )} = 0

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

1 + cot^{2} (x) - cot^{2} (x) cos^{2} (x) = 0

Rewrite using trig identities

csc^{2} (x) - cos^{2} (x) cot^{2} (x) = 0

Factor

csc^{2} (x) - cos^{2} (x) cot^{2} (x) : (csc (x) + cos (x) cot (x)) (csc (x) - cos (x) cot (x))

(csc (x) + cos (x) cot (x)) (csc (x) - cos (x) cot (x)) = 0

Solving each part separately

csc (x) + cos (x) cot (x) = 0 or csc (x) - cos (x) cot (x) = 0

csc (x) + cos (x) cot (x) = 0 :

No Solution

csc (x) - cos (x) cot (x) = 0 :

No Solution

Combine all the solutions

No Solution for x \in R

sin (2 p + 1) = - 1

y, a \cdot z = 5 sin (2 y)

sin^{3} (x) = sin^{2} (x)

2 sec^{2} (a) + tan^{2} (a) = 3

3 cos^{2} (x) + 4 cos (x) + 1 = 0

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