What is the general solution for cos(x)*sec(x)*cot^2(x)=csc^2(x) ?

The general solution for cos(x)*sec(x)*cot^2(x)=csc^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 >

cos(x)sec(x)cot^2(x)=csc^2(x)

cos (x) \cdot sec (x) \cdot cot^{2} (x) = csc^{2} (x)

No Solution for x \in R

Solution steps

cos (x) sec (x) cot^{2} (x) = csc^{2} (x)

Subtract

csc^{2} (x)

from both sides

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

Express with sin, cos

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

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

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

Solve by substitution

cos (x) = 1, cos (x) = - 1

cos (x) = 1 : x = 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

Since the equation is undefined for:

2 πn, π + 2 πn

No Solution for x \in R

2 sin (3 x) + 2 sin (x) = 0

(cos (x) - 1) (3 cot (x) + 1) = 0

4 cot (x) = 3 csc (x)

x, sin (2 x) - cos (x) = 0

sin (θ) = \frac{7}{15}

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