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

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

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

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

No Solution for x \in R

Solution steps

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

Subtract

tan^{2} (x)

from both sides

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

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

cos (t) = \frac{1}{2}

3 cos^{2} (x) + 8 sin (x) = 7

csc (x + 1 0^{\circ}) = 3

6 tan (x) = 18 cot (x)

9 cos (x) = 0

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