Question

Which of the following options are equal to ${\cos }^{2}A-{\sin }^{2}A$ ?

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

Answer 1

Answer: (A), (D)

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

We know that, ${\sin }^{2}A+{\cos }^{2}A=1.$
$1){\cos }^{2}A-{\sin }^{2}A=(1-{\sin }^{2}A)-{\sin }^{2}A$
$=1-2{\sin }^{2}A$

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