Chứng minh rằng:a) \(\tan x + \cot x = \dfrac{1}{{\sin x.\cos x}}\) b) \(\dfrac{{1 + \sin 2x - \cos 2x}}{{1 + \sin
Chứng minh rằng:
a) \(\tan x + \cot x = \dfrac{1}{{\sin x.\cos x}}\)
b) \(\dfrac{{1 + \sin 2x - \cos 2x}}{{1 + \sin 2x + \cos 2x}} = \tan x\)
a) \(\tan x + \cot x = \dfrac{1}{{\sin x.\cos x}}\)
\( \Leftrightarrow VT = \dfrac{{\sin x}}{{\cos x}} + \dfrac{{\cos x}}{{\sin x}} \Leftrightarrow VT = \dfrac{{{{\sin }^2}x + {{\cos }^2}x}}{{\sin x.\cos x}} \Leftrightarrow VT = \dfrac{1}{{\sin x.\cos x}} = VP\left( {dpcm} \right)\)
b) \(\dfrac{{1 + \sin 2x - \cos 2x}}{{1 + \sin 2x + \cos 2x}} = \tan x\)
\(\begin{array}{l} \Leftrightarrow VT = \dfrac{{1 + \sin 2x - \left( {1 - 2{{\sin }^2}x} \right)}}{{1 + \sin 2x + \left( {2{{\cos }^2}x - 1} \right)}} \Leftrightarrow VT = \dfrac{{2\sin x.\cos x + 2{{\sin }^2}x}}{{2\sin x.\cos x + 2{{\cos }^2}x}}\\ \Leftrightarrow VT = \dfrac{{2\sin x.\left( {\sin x + \cos x} \right)}}{{2\cos x.\left( {\sin x + \cos x} \right)}} \Leftrightarrow VT = \dfrac{{\sin x}}{{\cos x}} = \tan x = VP\left( {dpcm} \right)\end{array}\)
Hỗ trợ - Hướng dẫn
-
024.7300.7989
-
1800.6947
(Thời gian hỗ trợ từ 7h đến 22h)
Email: lienhe@tuyensinh247.com