To solve this problem, we need to evaluate both the Assertion (A) and Reason (R) given in the question.
Assertion (A): Melting point of Boron (2453 K) is unusually high in group 13 elements.
Reason (R): Solid Boron has a very strong crystalline lattice.
Given this logical analysis, both the assertion and the reason are correct, and the reason correctly explains the assertion.
The correct answer is: Both (A) and (R) are correct and (R) is the correct explanation of (A).
Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all \( x, y \in \mathbb{R}. \)
If \( f'(0) = \frac{1}{2} \), then the value of \( 24f''\left( \frac{5\pi}{3} \right) \) is: