Question

The value of $[{\cos }^{4}A-{\sin }^{4}A]$ is equal to:

• A. $2{\cos }^{2}A+1$
• B. $2{\cos }^{2}A-1$
• C. $2{\sin }^{2}A-1$
• D. $2{\sin }^{2}A+1$

Answer 1

The correct option is B $2{\cos }^{2}A-1$

${\cos }^{4}A-{\sin }^{4}A=({\cos }^{2}A-{\sin }^{2}A)({\cos }^{2}A+{\sin }^{2}A)$

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

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

$=2{\cos }^{2}A-1.$

Hence, the answer is $2{\cos }^{2}A-1.$