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

The general solution for tan^2(x)=sin(x)sec(x) is x= pi/4+pin,x=pin

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

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

x = \frac{π}{4} + πn, x = πn

Solution steps

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

Subtract

sin (x) sec (x)

from both sides

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

Rewrite using trig identities

- tan (x) + tan^{2} (x) = 0

Solve by substitution

tan (x) = 1, tan (x) = 0

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = 0 : x = πn

Combine all the solutions

x = \frac{π}{4} + πn, x = πn

cos (x) = - 6544

4 cosh (x) = 7

2 tan^{2} (x) - tan (x) = 0

4 \cdot cos^{2} (x) - 3 = 0

3 tan (x) - 2 = - 1

What is the general solution for tan^2(x)=sin(x)sec(x) ?
The general solution for tan^2(x)=sin(x)sec(x) is x= pi/4+pin,x=pin