Đáp án + Giải thích các bước giải:

Bài 22:

$A = (1 - \sin^2 x)\cot^2 x + (1 - \cot^2 x)$

$= \cot^2 x - \sin^2 x . \cot^2 x + 1 - \cot^2 x$

$= \cot^2 x - \cot^2 x + 1 - \cos^2 x$

$= 0 + \sin^2 x$

$= \sin^2 x$

Bài 23:

$A = \cos (5\pi - x) - \sin \bigg(\dfrac{3\pi}{2} + x\bigg) + \tan\bigg(\dfrac{3\pi}{2} - x\bigg)$

$= \cos (\pi + 2 . 2\pi - x) - \sin \bigg(x - \dfrac{\pi}{2} + 2\pi\bigg) + \tan \bigg(\pi + \dfrac{\pi}{2} - x\bigg)$

$= \cos (\pi - x) - \sin\bigg(x - \dfrac{\pi}{2}\bigg) + \tan\bigg(\dfrac{\pi}{2} - x\bigg)$

$=-\cos x + \sin \bigg(\dfrac{\pi}{2} - x\bigg) + \cot x$

$= -\cos x + \cos x + \cot x$

$= \cot x$