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

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

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sec(x)=sin^2(x)sec(x)

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

No Solution for x \in R

Solution steps

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

Subtract

sin^{2} (x) sec (x)

from both sides

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

Factor

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

- sec (x) (sin (x) + 1) (sin (x) - 1) = 0

Solving each part separately

sec (x) = 0 or sin (x) + 1 = 0 or sin (x) - 1 = 0

sec (x) = 0 :

No Solution

sin (x) + 1 = 0 : x = \frac{3 π}{2} + 2 πn

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Since the equation is undefined for:

\frac{3 π}{2} + 2 πn, \frac{π}{2} + 2 πn

No Solution for x \in R

cos (5 t) - cos (3 t) = sin (4 t)

2 sin^{2} (θ) - 1 = 0, 0 \leq θ < 2 π

2 cosh (2 x) = 5 sinh (x) + 3

tan (x) = \frac{6.9}{6.6}

sin (x) - cos (x) = \frac{2}{2}

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