What is the limit as θ approaches pi/3 of (tan(θ))/(sin^2(θ)) ?

The limit as θ approaches pi/3 of (tan(θ))/(sin^2(θ)) is 4/(sqrt(3))

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limit as θ approaches pi/3 of (tan(θ))/(sin^2(θ))

θ \to \frac{π}{3} lim (\frac{tan ( θ )}{sin ^{2} ( θ )})

\frac{4}{3}

Decimal

2.30940 \dots

Solution steps

θ \to \frac{π}{3} lim (\frac{tan ( θ )}{sin ^{2} ( θ )})

Plug in the value

θ = \frac{π}{3}

= \frac{tan ( \frac{π}{3} )}{sin ^{2} ( \frac{π}{3} )}

Simplify

\frac{tan ( \frac{π}{3} )}{sin ^{2} ( \frac{π}{3} )} : \frac{4}{3}

= \frac{4}{3}

What is the limit as θ approaches pi/3 of (tan(θ))/(sin^2(θ)) ?
The limit as θ approaches pi/3 of (tan(θ))/(sin^2(θ)) is 4/(sqrt(3))