What is the limit as θ approaches pi/6 of (sin(2θ))/(sin(θ)tan(θ)) ?

The limit as θ approaches pi/6 of (sin(2θ))/(sin(θ)tan(θ)) is 3

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limit as θ approaches pi/6 of (sin(2θ))/(sin(θ)tan(θ))

θ \to \frac{π}{6} lim (\frac{sin ( 2 θ )}{sin ( θ ) tan ( θ )})

3

Solution steps

θ \to \frac{π}{6} lim (\frac{sin ( 2 θ )}{sin ( θ ) tan ( θ )})

Plug in the value

θ = \frac{π}{6}

= \frac{sin ( 2 \cdot \frac{π}{6} )}{sin ( \frac{π}{6} ) tan ( \frac{π}{6} )}

Simplify

\frac{sin ( 2 \cdot \frac{π}{6} )}{sin ( \frac{π}{6} ) tan ( \frac{π}{6} )} : 3

= 3

x \to \infty lim (40)

x \to 2 - lim (ln (4 - x^{2}))

x \to 0 lim (x^{2} cos (\frac{π}{x}))

x \to 0 lim (- 1 + ln (x) x)

x \to \infty lim (\frac{sin ( 3 x )}{sin ( 4 x )})

What is the limit as θ approaches pi/6 of (sin(2θ))/(sin(θ)tan(θ)) ?
The limit as θ approaches pi/6 of (sin(2θ))/(sin(θ)tan(θ)) is 3