What is the general solution for csc(x)sec(x)=tan(x) ?

The general solution for csc(x)sec(x)=tan(x) is No Solution for x\in\mathbb{R}

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csc(x)sec(x)=tan(x)

csc (x) sec (x) = tan (x)

No Solution for x \in R

Solution steps

csc (x) sec (x) = tan (x)

Subtract

tan (x)

from both sides

csc (x) sec (x) - tan (x) = 0

Express with sin, cos

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

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

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

Solve by substitution

sin (x) = 1, sin (x) = - 1

sin (x) = 1 : x = \frac{π}{2} + 2 πn

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

Combine all the solutions

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

Since the equation is undefined for:

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

No Solution for x \in R

sin^{4} (x) = 1 - cos^{4} (x)

8 cos (\frac{1}{2} x) + 4 = 0

5 sin (2 t) = 0

3 tan (3 x) + 3 = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

2 tan (θ) + 4 = tan (θ) + 5

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