Evaluate the following limit : lim(θ→0) (sin 3θ)/(tan 2θ)

Question

Evaluate the following limit : \(\lim\limits_{\theta \to0}\cfrac{sin\,3\theta}{tan\,2\theta} \)

lim(θ→0) (sin 3θ)/(tan 2θ)

Answer 1

To find: \(\lim\limits_{\theta \to0} \cfrac{sin\,3\theta}{tan\,2\theta}\) 

\(\lim\limits_{\theta \to0} \cfrac{sin\,3\theta}{tan\,2\theta}\) 

Multiplying and Dividing by 3θ in numerator & Multiplying and Dividing by 2θ in the denominator:

Now, put 3θ = y and 2θ = t

Hence, the value of \(\lim\limits_{\theta \to0} \cfrac{sin\,3\theta}{tan\,2\theta}\) = \(\cfrac32\)