Toán cos^2x(cos^2x+2sin^2x+sin^2x tan^2x) rút gọn 20/10/2021 By Julia cos^2x(cos^2x+2sin^2x+sin^2x tan^2x) rút gọn
$\cos^2x(\cos^2x+2\sin^2x+\sin^2x\tan^2x)$ $=\cos^2x(1+\sin^2x+\sin^2x\tan^2x)$ $=\cos^2x[1+\sin^2x(1+\tan^2x)]$ $=\cos^2x\Big(1+\sin^2x.\dfrac{1}{\cos^2x}\Big)$ $=\cos^2x(1+\tan^2x)$ $=\cos^2x+\cos^2x.\tan^2x$ $=\cos^2x+\sin^2x$ $=1$ Trả lời
Đáp án:
Giải thích các bước giải:
$\cos^2x(\cos^2x+2\sin^2x+\sin^2x\tan^2x)$
$=\cos^2x(1+\sin^2x+\sin^2x\tan^2x)$
$=\cos^2x[1+\sin^2x(1+\tan^2x)]$
$=\cos^2x\Big(1+\sin^2x.\dfrac{1}{\cos^2x}\Big)$
$=\cos^2x(1+\tan^2x)$
$=\cos^2x+\cos^2x.\tan^2x$
$=\cos^2x+\sin^2x$
$=1$