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

The general solution for tan^2(x)+2sec(x)+2=0 is x=pi+2pin

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tan^2(x)+2sec(x)+2=0

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

x = π + 2 πn

Solution steps

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

Rewrite using trig identities

1 + sec^{2} (x) + 2 sec (x) = 0

Solve by substitution

sec (x) = - 1

sec (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = π + 2 πn

sin (θ) = 1 + cos (θ)

7 cos (2 x) = 7 cos^{2} (x) - 3

- cos^{2} (θ) + 1 = 0

cos^{2} (x) - \frac{1}{4} = 0, 0 \leq x \leq 2 π

tan (6 x) = 1

What is the general solution for tan^2(x)+2sec(x)+2=0 ?
The general solution for tan^2(x)+2sec(x)+2=0 is x=pi+2pin