Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
A = {\left( {\tan x + {\mathop{\rm cotx}\nolimits} } \right)^2} - {\left( {\tan x + {\mathop{\rm cotx}\nolimits} } \right)^2} = 0\\
B = {\left( {\sin x - {\mathop{\rm cosx}\nolimits} } \right)^2} + {\left( {\sin x + \cos x} \right)^2}\\
= {\sin ^2}x - 2\sin x.\cos x + {\cos ^2}x + {\sin ^2}x + 2\sin x\cos x + {\cos ^2}x\\
= 2\left( {{{\sin }^2}x + {{\cos }^2}x} \right)\\
= 2.1 = 2\\
C = {\sin ^2}x.\tan x + {\cos ^2}x.{\mathop{\rm cotx}\nolimits} + 2sinx.cosx\\
= \frac{{{{\sin }^3}x}}{{\cos x}} + \frac{{{{\cos }^3}x}}{{\sin x}} + 2sinx.cosx\\
= \frac{{{{\sin }^4}x + {{\cos }^4}x}}{{\sin x\cos x}} + 2\sin x.\cos x\\
= \frac{{{{\left( {{{\sin }^2}x + {{\cos }^2}x} \right)}^2} - 2{{\sin }^2}x.{{\cos }^2}x}}{{\sin x\cos x}} + 2\sin x\cos x\\
= \frac{1}{{\sin x\cos x}} - 2\sin x\cos x + 2\sin x\cos x\\
= \frac{1}{{\sin x\cos x}}
\end{array}\)
