What is 1/(sqrt(tan^2(x)+1)) ?

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

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simplify 1/(sqrt(tan^2(x)+1))

simplify

\frac{1}{tan ^{2} ( x ) + 1}

cos (x)

Solution steps

\frac{1}{tan ^{2} ( x ) + 1}

Rewrite using trig identities

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

Express with sin, cos

= cos^{2} (x)

Apply radical rule:

assuming

a \geq 0

= cos (x)

cos (\cdot arccos (x))

x d x + sec (x) sin (x)

cos (arcsin (\frac{m g}{T}))

sec (\frac{- 7 x}{6})

\frac{sin ( θ )}{cos ^{2} ( θ )} d θ