Question

The value of ${\cos }^2{75}^o+{\cos }^2{45}^o+{\cos }^2{15}^0-{\cos }^2{30}^o-{\cos }^2{60}^o$ is

• A. $0$
• B. $1$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{1}{2}$

${\cos }^2{75}^o+{\cos }^2{45}^o+{\cos }^2{15}^0-{\cos }^2{30}^o-{\cos }^2{60}^o$

$\Rightarrow {\cos }^2(90-15{)}^o+{\cos }^2{15}^o+{\cos }^2{45}^o-({\cos }^2(90-60{)}^o+{\cos }^2{60}^o)$

$={\sin }^2{15}^o+{\cos }^2{15}^o+{\cos }^4{5}^o-({\cos }^2{60}^o+{\sin }^2{60}^o)$

$=1+\frac{1}{2}-1=\frac{1}{2}$

Therefore, Answer is $\frac{1}{2}$