What is the general solution for 0=sec^2(x)e^{tan(x)}(2tan(x)+sec^2(x)) ?

The general solution for 0=sec^2(x)e^{tan(x)}(2tan(x)+sec^2(x)) is x=(3pi)/4+pin

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0=sec^2(x)e^{tan(x)}(2tan(x)+sec^2(x))

0 = sec^{2} (x) e^{t a n (x)} (2 tan (x) + sec^{2} (x))

x = \frac{3 π}{4} + πn

Solution steps

0 = sec^{2} (x) e^{t a n (x)} (2 tan (x) + sec^{2} (x))

Switch sides

sec^{2} (x) e^{t a n (x)} (2 tan (x) + sec^{2} (x)) = 0

Rewrite using trig identities

(1 + tan^{2} (x)) (1 + tan^{2} (x) + 2 tan (x)) e^{t a n (x)} = 0

Solve by substitution

tan (x) = - 1

tan (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = \frac{3 π}{4} + πn

tan (x) = 3, - 18 0^{\circ} < x < 18 0^{\circ}

cot^{2} (t) csc (t) = sin (t)

\frac{6}{12} = cos (θ)

sin (a) = \frac{6.88}{6.9}

sin (x) = cos (3 2^{\circ})

What is the general solution for 0=sec^2(x)e^{tan(x)}(2tan(x)+sec^2(x)) ?
The general solution for 0=sec^2(x)e^{tan(x)}(2tan(x)+sec^2(x)) is x=(3pi)/4+pin