What is the general solution for solvefor f,r= 8/(sec(f^0)) ?

The general solution for solvefor f,r= 8/(sec(f^0)) is No Solution for f\in\mathbb{R}

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solvefor f,r= 8/(sec(f^0))

solve for

f, r = \frac{8}{sec ( f ^{0} )}

No Solution for f \in R

Solution steps

r = \frac{8}{sec ( f ^{0} )}

Switch sides

\frac{8}{sec ( f ^{0} )} = r

Multiply both sides by

sec (f^{0})

\frac{8}{sec ( f ^{0} )} = r

Multiply both sides by

sec (f^{0})

\frac{8}{sec ( f ^{0} )} sec (f^{0}) = r sec (f^{0})

Simplify

8 = r sec (f^{0})

8 = r sec (f^{0})

Switch sides

r sec (f^{0}) = 8

Divide both sides by

r; r \neq = 0

r sec (f^{0}) = 8

Divide both sides by

r; r \neq = 0

\frac{r sec ( f ^{0} )}{r} = \frac{8}{r}; r \neq = 0

Simplify

sec (f^{0}) = \frac{8}{r}; r \neq = 0

sec (f^{0}) = \frac{8}{r}; r \neq = 0

Apply trig inverse properties

sec (f^{0}) = \frac{8}{r}

General solutions for

sec (f^{0}) = \frac{8}{r}

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = - arcsec (a) + 2 πn

f^{0} = arcsec (\frac{8}{r}) + 2 πn, f^{0} = - arcsec (\frac{8}{r}) + 2 πn

f^{0} = arcsec (\frac{8}{r}) + 2 πn, f^{0} = - arcsec (\frac{8}{r}) + 2 πn

Solve

f^{0} = arcsec (\frac{8}{r}) + 2 πn :

True for all

f; 1 = arcsec (\frac{8}{r}) + 2 πn

f^{0} = arcsec (\frac{8}{r}) + 2 πn

Apply rule

a^{0} = 1, a \neq = 0

1 = arcsec (\frac{8}{r}) + 2 πn

Both sides are equal

True for all f; 1 = arcsec (\frac{8}{r}) + 2 πn

Solve

f^{0} = - arcsec (\frac{8}{r}) + 2 πn :

True for all

f; 1 = - arcsec (\frac{8}{r}) + 2 πn

f^{0} = - arcsec (\frac{8}{r}) + 2 πn

Apply rule

a^{0} = 1, a \neq = 0

1 = - arcsec (\frac{8}{r}) + 2 πn

Both sides are equal

True for all f; 1 = - arcsec (\frac{8}{r}) + 2 πn

f = True for all f, f = True for all f

Since the equation is undefined for:

True for all

f

No Solution for f \in R

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What is the general solution for solvefor f,r= 8/(sec(f^0)) ?
The general solution for solvefor f,r= 8/(sec(f^0)) is No Solution for f\in\mathbb{R}