What is 1/(sqrt(1+tan^2(θ))) ?

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

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simplify 1/(sqrt(1+tan^2(θ)))

simplify

\frac{1}{1 + tan ^{2} ( θ )}

cos (θ)

Solution steps

\frac{1}{1 + tan ^{2} ( θ )}

Rewrite using trig identities

= \frac{1}{sec ^{2} ( θ )}

Express with sin, cos

= cos^{2} (θ)

Apply radical rule:

assuming

a \geq 0

= cos (θ)

sin (x + \frac{2 π}{3})

sin (27 0^{\circ} + θ)

sin (x - \frac{2 π}{3})

- cos (x + π)

cos (55 \frac{π}{2} - x)