limlimitsθ→ 0(sin 2θ)/(2θ)= ____. (a) 1 (b) ∞ (c) 2 (d) 0

Question 45 of 49

\lim\limits_{\theta\to 0}\dfrac{\sin 2\theta}{2\theta}=

(a)

1

(b)

\infty

(c)

2

(d)

0

Puducherry TnboardTamil Nadu HSC First Year (DGE) Commerce Board 2025MCQ· 1mImportance★★★★★

92% · 45/49 Questions

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

This is the standard trigonometric limit form $\dfrac{\sin(\text{angle})}{\text{same angle}}\to 1$ , so the value is $1$ .

The fundamental trigonometric limit is

$\lim_{t\to 0}\frac{\sin t}{t}=1.$

Here let $t=2\theta$ . As $\theta\to 0$ , also $t\to 0$ , and the numerator's angle ( $2\theta$ ) exactly matches the denominator ( $2\theta$ ): …

Q. $\lim\limits_{\theta\to 0}\dfrac{\sin 2\theta}{2\theta}=$ ________.