Question

Solve ${\cos }^{4}A-{\sin }^{4}A+1-2{\cos }^{2}A$

Answer 1

${\cos }^{4}A-{\sin }^{4}A+1-2{\cos }^{2}A$

$=({\cos }^{2}A+{\sin }^{2}A)({\cos }^{2}A-{\sin }^{2}A)+1-2{\cos }^{2}A$

$=2{\cos }^{2}A-1+1-2{\cos }^{2}A$ ( As ${\cos }^{2}A+{\sin }^A=1,1-{\cos }^{2}A={\sin }^{2}A$)

$=0$