What is the general solution for sec^2(θ)-2=tan^2(θ) ?

The general solution for sec^2(θ)-2=tan^2(θ) is No Solution for θ\in\mathbb{R}

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sec^2(θ)-2=tan^2(θ)

sec^{2} (θ) - 2 = tan^{2} (θ)

No Solution for θ \in R

Solution steps

sec^{2} (θ) - 2 = tan^{2} (θ)

Subtract

tan^{2} (θ)

from both sides

sec^{2} (θ) - 2 - tan^{2} (θ) = 0

Express with sin, cos

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

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

1 - sin^{2} (θ) - 2 cos^{2} (θ) = 0

Rewrite using trig identities

- cos^{2} (θ) = 0

Divide both sides by

- 1

cos (θ) = 0

General solutions for

cos (θ) = 0

θ = \frac{π}{2} + 2 πn, θ = \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 θ \in R

cos (x) = sin (x) + 1

2 sin^{2} (θ) = 3 (1 - cos (- θ))

sec (x) - 2 = 0

2 sin^{4} (x) + sin^{2} (x) - 1 = 0

tan (\frac{x}{9}) + 3 = 0

What is the general solution for sec^2(θ)-2=tan^2(θ) ?
The general solution for sec^2(θ)-2=tan^2(θ) is No Solution for θ\in\mathbb{R}