What is sqrt(1/(cos^2(x))) ?

The solution to sqrt(1/(cos^2(x))) is sec(x)

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simplify sqrt(1/(cos^2(x)))

simplify

\frac{1}{cos ^{2} ( x )}

sec (x)

Solution steps

\frac{1}{cos ^{2} ( x )}

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

Apply radical rule:

assuming

a \geq 0

cos^{2} (x) = cos (x)

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

Apply rule

1 = 1

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

Rewrite using trig identities

= sec (x)

arcsec (\frac{1}{cos ( θ )})

\frac{1}{sin ^{2} ( t )} - 1

\frac{- 2 cos ( nπ )}{n} sin (n x)

sin (θ) - sin (\frac{π}{2} - θ)

cos (9 π + a)