What is the general solution for tan^2(x)=sec^2(x)+1 ?

The general solution for tan^2(x)=sec^2(x)+1 is No Solution for x\in\mathbb{R}

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tan^2(x)=sec^2(x)+1

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

No Solution for x \in R

Solution steps

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

Subtract

sec^{2} (x) + 1

from both sides

tan^{2} (x) - sec^{2} (x) - 1 = 0

Express with sin, cos

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

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

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

Rewrite using trig identities

- 1 - cos (2 x) = 0

Move

1

to the right side

- cos (2 x) = 1

Divide both sides by

- 1

cos (2 x) = - 1

General solutions for

cos (2 x) = - 1

2 x = π + 2 πn

Solve

2 x = π + 2 πn : x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

Since the equation is undefined for:

\frac{π}{2} + πn

No Solution for x \in R

12 = 3 sec (θ) + 5 csc (θ)

tan^{2} (4 (x + \frac{π}{2})) = 3

sin (9 x + 2) = cos (6 x - 7)

2 cos (3 x + \frac{π}{2}) = - 1

sin (\frac{3 θ}{2}) = 0

What is the general solution for tan^2(x)=sec^2(x)+1 ?
The general solution for tan^2(x)=sec^2(x)+1 is No Solution for x\in\mathbb{R}