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

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

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

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

No Solution for x \in R

Solution steps

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

Subtract

sec (x)

from both sides

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

Simplify

\frac{1 + tan ^{2} ( x )}{1 + sec ( x )} - sec (x) : \frac{1 + tan ^{2} ( x ) - sec ( x ) ( 1 + sec ( x ) )}{1 + sec ( x )}

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

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

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

Rewrite using trig identities

- sec (x) = 0

Divide both sides by

- 1

sec (x) = 0

sec (x) \leq - 1 or sec (x) \geq 1

No Solution for x \in R

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

sin (5 x - 1) = \frac{4}{5}

sin^{2} (x) = \frac{1}{36}

tan (x) = 31

sin^{4} (x) + cos^{2} (x) = 2

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