Question

Write the value of 2 (sin⁶ x + cos⁶ x) −3 (sin⁴ x + cos⁴ x) + 1.

Answer 1

$$\begin{gathered} 2\left({\sin }^{6}x+{\cos }^{6}x\right)-3\left({\sin }^{4}x+{\cos }^{4}x\right)+1 \\ =2\left({\sin }^{2}x+{\cos }^{2}x\right)\left({\sin }^{4}x+{\cos }^{4}x-{\sin }^{2}x.c{\mathrm{os}}^{2}x\right)-3\left({\sin }^{4}x+{\cos }^{4}x\right)+1 \\ =2.1\left({\sin }^{4}x+{\cos }^{4}x-{\sin }^{2}x.c{\mathrm{os}}^{2}x\right)-3\left({\sin }^{4}x+{\cos }^{4}x\right)+1 \\ =2\left({\sin }^{4}x+{\cos }^{4}x\right)-2{\sin }^{2}x.c{\mathrm{os}}^{2}x-3\left({\sin }^{4}x+{\cos }^{4}x\right)+1 \\ =-\left({\sin }^{4}x+{\cos }^{4}x\right)-2{\sin }^{2}x.c{\mathrm{os}}^{2}x+1 \\ =-\left\{{\sin }^{4}x+{\cos }^{4}x+2{\sin }^{2}x.c{\mathrm{os}}^{2}x\right\}+1 \\ =-{\left({\sin }^{2}x+{\cos }^{2}x\right)}^2+1 \\ =-1+1 \\ =0 \end{gathered}$$