Question

${\cos }^2{9}^0+{\cos }^2{18}^0+{\cos }^2{7}^o+...+{\cos }^2{81}^0=$

• A. $4$
• B. $\frac{9}{2}$
• C. $5$
• D. $\frac{11}{2}$

Answer 1

The correct option is B $\frac{9}{2}$

${\cos }^2{9}^o+{\cos }^2{18}^o+{\cos }^2{27}^o+{\cos }^2{36}^o+{\cos }^2{45}^o+{\cos }^2{54}^o+{\cos }^2{63}^o+{\cos }^2{72}^o+{\cos }^2{81}^o={\cos }^2{9}^o+{\cos }^2{18}^o+{\cos }^2{27}^o+{\cos }^2{36}^o+{\cos }^2{45}^o+{\cos }^2(90-36{)}^o+{\cos }^2(90-27{)}^o+{\cos }^2(90-18{)}^o+{\cos }^2(90-9{)}^o$

$={\cos }^2{9}^o+{\cos }^2{18}^o+{\cos }^2{27}^o+{\cos }^2{36}^o+{\cos }^2{45}^o+{\sin }^2{36}^o+{\sin }^2{27}^o+{\sin }^2{18}^o+{\sin }^2{9}^o=({\sin }^2{9}^o+{\cos }^2{9}^o)+({\sin }^2{18}^o+{\cos }^2{18}^o)+({\sin }^2{27}^o+{\cos }^2{27}^o)+({\sin }^2{36}^o+{\cos }^2{36}^o)+{\cos }^2{45}^o=1+1+1+1+\frac{1}{2}=\frac{9}{2}$

Therefore, Answer is $\frac{9}{2}$