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

The general solution for tan^2(x)-sec^2(x)=cos(-x) is x=-pi-2pin

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tan^2(x)-sec^2(x)=cos(-x)

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

x = - π - 2 πn

Degrees

x = - 18 0^{\circ} - 36 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

= - 1

- 1 = cos (- x)

Switch sides

cos (- x) = - 1

General solutions for

cos (- x) = - 1

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

- x = π + 2 πn

- x = π + 2 πn

Solve

- x = π + 2 πn : x = - π - 2 πn

- x = π + 2 πn

Divide both sides by

- 1

- x = π + 2 πn

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{π}{- 1} + \frac{2 πn}{- 1}

Simplify

\frac{- x}{- 1} = \frac{π}{- 1} + \frac{2 πn}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{π}{- 1} + \frac{2 πn}{- 1} : - π - 2 πn

\frac{π}{- 1} + \frac{2 πn}{- 1}

\frac{π}{- 1} = - π

\frac{π}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{π}{1}

Apply rule

\frac{a}{1} = a

= - π

= - π + \frac{2 πn}{- 1}

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 πn}{1}

Apply rule

\frac{a}{1} = a

= - 2 πn

= - π - 2 πn

x = - π - 2 πn

x = - π - 2 πn

x = - π - 2 πn

x = - π - 2 πn

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

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

- 2 + cos (θ) = - 2 + \frac{6}{5} \cdot cos (θ)

tan^{2} (y) + 3 - 2 sec^{2} (y) = 0

500 = 538.5 cos (x - 1 0^{\circ})

What is the general solution for tan^2(x)-sec^2(x)=cos(-x) ?
The general solution for tan^2(x)-sec^2(x)=cos(-x) is x=-pi-2pin