## Thomas' Calculus 13th Edition

$\sin{\left(x+\dfrac{\pi}{2} \right)} = \cos{x} = \text{ RHS}$
Addition formula $$\sin{(A+B)}= \sin{A} \cos{B} +\cos{A} \sin{B}$$ $\therefore \sin{\left(x+\dfrac{\pi}{2} \right)} = \sin{x} \cos{\left(\dfrac{\pi}{2} \right)} +\cos{x} \sin{\left(\dfrac{\pi}{2} \right)}$ $\sin{\left(x+\dfrac{\pi}{2} \right)} = \sin{x} \times (0) + \cos{x} \times (1)$ $\sin{\left(x+\dfrac{\pi}{2} \right)} = \cos{x} = \text{ RHS}$