Đơn giản biểu thức \(B = \frac{{{{\cos }^2}x - {{\sin }^2}x}}{{{{\cot }^2}x - {{\tan }^2}x}} - {\cos ^2}x\).
Sử dụng \(\tan x = \frac{{\sin x}}{{\cos x}},{\mkern 1mu} {\mkern 1mu} \cot x = \frac{{\cos x}}{{\sin x}}\), quy đồng, sử dụng hằng đẳng thức để rút gọn.
\(\begin{array}{*{20}{l}}{B = \frac{{{{\cos }^2}x - {{\sin }^2}x}}{{{{\cot }^2}x - {{\tan }^2}x}} - {{\cos }^2}x}\\{B = \frac{{{{\cos }^2}x - {{\sin }^2}x}}{{\frac{{{{\cos }^2}x}}{{{{\sin }^2}x}} - \frac{{{{\sin }^2}x}}{{{{\cos }^2}x}}}} - {{\cos }^2}x}\\{B = \frac{{{{\cos }^2}x - {{\sin }^2}x}}{{\frac{{{{\cos }^4}x - {{\sin }^4}x}}{{{{\sin }^2}x{{\cos }^2}x}}}} - {{\cos }^2}x}\\{B = \frac{{\left( {{{\cos }^2}x - {{\sin }^2}x} \right){{\sin }^2}x{{\cos }^2}x}}{{\left( {{{\cos }^2}x - {{\sin }^2}x} \right)\left( {{{\cos }^2}x + {{\sin }^2}x} \right)}} - {{\cos }^2}x}\\{B = {{\sin }^2}x{{\cos }^2}x - {{\cos }^2}x}\\{B = {{\cos }^2}x\left( {{{\sin }^2}x - 1} \right)}\\{B = - {{\cos }^4}x}\end{array}\)
