What is (-cos(x))/(cos^2(x)) ?

The solution to (-cos(x))/(cos^2(x)) is -sec(x)

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simplify (-cos(x))/(cos^2(x))

simplify

\frac{- cos ( x )}{cos ^{2} ( x )}

- sec (x)

Solution steps

\frac{- cos ( x )}{cos ^{2} ( x )}

Apply the fraction rule:

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

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

Cancel the common factor:

cos (x)

= - \frac{1}{cos ( x )}

Rewrite using trig identities

= - sec (x)

sin (arccos (\frac{12}{x}))

tan (arcsec (x))

tan (2 x + \frac{π}{2})

tan (\frac{π}{2} - x) tan (x)

cos (\frac{π}{2} - x) - sin (x)