Question

Evaluate ${\cos }^2{13}^o-{\sin }^2{77}^o$

Answer 1

Consider $\cos {13}^0$ which can be rewritten as follows:

$\cos {13}^0=\cos {({90}^0-77}^0)=\sin {77}^0$ $(\because \cos ({90}^0-x)=\sin x)$

Since $\cos {13}^0=\sin {77}^0$, thus ${\cos }^2{13}^0={\sin }^2{77}^0$.

Therefore, ${\cos }^2{13}^0-{\sin }^2{77}^0$ can be evaluated as shown below:

${\cos }^2{13}^0-{\sin }^2{77}^0={\sin }^2{77}^0-{\sin }^2{77}^0=0$

Hence, ${\cos }^2{13}^0-{\sin }^2{77}^0=0$.