Biểu thức C = 2(sin^4 x + cos^4 x + sin^2 x cos^2 x)^2 - (sin^8 x + cos^8 x

* Hướng dẫn giải

Đáp án C

Ta có:

$$\begin{gathered} C=2\left({\sin }^{4}x+co{s}^{4}x+{\sin }^{2}xco{s}^{2}x\right){}^2-\left({\sin }^{8}x+co{s}^{8}x\right) \\ =2{\left[{\left({\sin }^{2}x+co{s}^{2}x\right)}^2-{\sin }^{2}xco{s}^{2}x\right]}^2-\left[{\left({\sin }^{4}x+co{s}^{4}x\right)}^2-2{\sin }^{4}xco{s}^{4}x\right] \\ =2{\left[1-{\sin }^{2}xco{s}^{2}x\right]}^2-\left[{\left({\sin }^{2}x+co{s}^{2}x\right)}^2-2{\sin }^{2}xco{s}^{2}x\right]{}^2+2{\sin }^{4}xco{s}^{4}x \\ =2{\left[1-{\sin }^{2}xco{s}^{2}x\right]}^2-\left[1-2{\sin }^{2}x.co{s}^{2}x\right]{}^2+2{\sin }^{4}xco{s}^{4}x \\ =2\left(1-2{\sin }^{2}xco{s}^{2}x+{\sin }^{4}xco{s}^{4}x\right)-\left(1-4{\sin }^{2}xco{s}^{2}x+4{\sin }^{4}xco{s}^{4}x\right)+2{\sin }^{4}xco{s}^{4}x \\ =1 \end{gathered}$$