What is the general solution for sec^2(x)-2=tan^2(x),0<= x<= 2pi ?

The general solution for sec^2(x)-2=tan^2(x),0<= x<= 2pi is No Solution for x\in\mathbb{R}

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sec^2(x)-2=tan^2(x),0<= x<= 2pi

sec^{2} (x) - 2 = tan^{2} (x), 0 \leq x \leq 2 π

No Solution for x \in R

Solution steps

sec^{2} (x) - 2 = tan^{2} (x), 0 \leq x \leq 2 π

Subtract

tan^{2} (x)

from both sides

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

Express with sin, cos

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

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

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

Rewrite using trig identities

- cos^{2} (x) = 0

Divide both sides by

- 1

cos (x) = 0

General solutions for

cos (x) = 0

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solutions for the range

0 \leq x \leq 2 π

x = \frac{π}{2}, x = \frac{3 π}{2}

Since the equation is undefined for:

\frac{π}{2}, \frac{3 π}{2}

No Solution for x \in R

sin (\frac{1}{2} x) = - \frac{1}{2}

4 cos (x) - 3 cos (x) - 1 = 0

3 sin (6 0^{\circ} - \frac{3 x}{4}) = 5 sin (\frac{3 x}{4} - 3 0^{\circ})

tan (u) = \frac{3}{3}

\frac{sin ( θ )}{60} = \frac{sin ( 8 0 ^{\circ} )}{280.87}

What is the general solution for sec^2(x)-2=tan^2(x),0<= x<= 2pi ?
The general solution for sec^2(x)-2=tan^2(x),0<= x<= 2pi is No Solution for x\in\mathbb{R}