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

sec (x)

from both sides

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

Factor

sin^{2} (x) sec (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 (θ) = - 0.07

cos (θ) = - 0.29

sin (x) - 7 = cos (x) - 7

tan (a) = \frac{15}{8}

cot^{2} (x) = - cot (x)

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}