What is 2/(sqrt(1+tan^2(θ))) ?

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

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simplify 2/(sqrt(1+tan^2(θ)))

simplify

\frac{2}{1 + tan ^{2} ( θ )}

2 cos (θ)

Solution steps

\frac{2}{1 + tan ^{2} ( θ )}

Rewrite using trig identities

= \frac{2}{sec ^{2} ( θ )}

Express with sin, cos

= 2 cos^{2} (θ)

cos^{2} (θ) = cos (θ)

= 2 cos (θ)

cos (x - 2 π)

cos (x - \frac{π}{6})

sin (arcsin (\frac{x}{3}))

cos (x + 4 5^{\circ})

1 + cot^{2} (x)