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

The general solution for sin^2(x)*sec(x)=(sin^2(x))/(cot(x)) is No Solution for x\in\mathbb{R}

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sin^2(x)*sec(x)=(sin^2(x))/(cot(x))

sin^{2} (x) \cdot sec (x) = \frac{sin ^{2} ( x )}{cot ( x )}

No Solution for x \in R

Solution steps

sin^{2} (x) sec (x) = \frac{sin ^{2} ( x )}{cot ( x )}

Subtract

\frac{sin ^{2} ( x )}{cot ( x )}

from both sides

sin^{2} (x) sec (x) - \frac{sin ^{2} ( x )}{cot ( x )} = 0

Simplify

sin^{2} (x) sec (x) - \frac{sin ^{2} ( x )}{cot ( x )} : \frac{sin ^{2} ( x ) sec ( x ) cot ( x ) - sin ^{2} ( x )}{cot ( x )}

\frac{sin ^{2} ( x ) sec ( x ) cot ( x ) - sin ^{2} ( x )}{cot ( x )} = 0

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

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

Factor

sin^{2} (x) sec (x) cot (x) - sin^{2} (x) : sin^{2} (x) (sec (x) cot (x) - 1)

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

Solving each part separately

sin^{2} (x) = 0 or sec (x) cot (x) - 1 = 0

sin^{2} (x) = 0 : x = 2 πn, x = π + 2 πn

sec (x) cot (x) - 1 = 0 :

No Solution

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 tan (θ) + sin (θ) cos (θ) = 0

sec (x) = \frac{25}{7}

sin (\frac{x}{2}) = \frac{1}{2} sin (x)

tan (θ) = \frac{- 3}{3}

csc (2 θ) = \frac{1}{2} (sec (θ)) (cos (θ))

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