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

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

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

simplify

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

cos (x)

Solution steps

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

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)

csc (27 0^{\circ} + x)

tan (2 (x - \frac{π}{2})) + 1

cos (θ - \frac{π}{4})

tan (arcsec (\frac{x}{0.1}))

sin (θ + \frac{π}{3})