(cos27-cos63)/(cos27+cos63)  এর মান নির্ণয় কর।

Explanation:

Another Explanation (5): ```html \( \frac{\cos 27^\circ - \cos 63^\circ}{\cos 27^\circ + \cos 63^\circ} \) 🤓 আমরা জানি, \( \cos C - \cos D = -2 \sin \frac{C+D}{2} \sin \frac{C-D}{2} \) এবং \( \cos C + \cos D = 2 \cos \frac{C+D}{2} \cos \frac{C-D}{2} \) 🤔 সুতরাং, \( \frac{\cos 27^\circ - \cos 63^\circ}{\cos 27^\circ + \cos 63^\circ} = \frac{-2 \sin \frac{27^\circ + 63^\circ}{2} \sin \frac{27^\circ - 63^\circ}{2}}{2 \cos \frac{27^\circ + 63^\circ}{2} \cos \frac{27^\circ - 63^\circ}{2}} \) ✨ \( = \frac{-2 \sin \frac{90^\circ}{2} \sin \frac{-36^\circ}{2}}{2 \cos \frac{90^\circ}{2} \cos \frac{-36^\circ}{2}} \) 🤩 \( = \frac{-2 \sin 45^\circ \sin (-18^\circ)}{2 \cos 45^\circ \cos (-18^\circ)} \) 😎 আমরা জানি, \( \sin (-x) = - \sin x \) এবং \( \cos (-x) = \cos x \) 😉 \( = \frac{-2 \sin 45^\circ (-\sin 18^\circ)}{2 \cos 45^\circ \cos 18^\circ} \) 🥳 \( = \frac{\sin 45^\circ \sin 18^\circ}{\cos 45^\circ \cos 18^\circ} \) 🤫 \( = \frac{\sin 45^\circ}{\cos 45^\circ} \cdot \frac{\sin 18^\circ}{\cos 18^\circ} \) 🤓 আমরা জানি, \( \frac{\sin x}{\cos x} = \tan x \) এবং \( \sin 45^\circ = \cos 45^\circ \) সুতরাং \( \frac{\sin 45^\circ}{\cos 45^\circ} = 1 \)। \( = 1 \cdot \tan 18^\circ \) 😇 \( = \tan 18^\circ \) 🎉 ```