Question

The value of ${\cos }^2{73}^o+{\cos }^2{47}^o-{\sin }^2{43}^o+{\sin }^2{107}^o$ is equal to :

• A. $1$
• B. $\frac{1}{2}$
• C. $\frac{\sqrt{3}}{2}$
• D. ${\sin }^2{73}^o+{\cos }^2{43}^o$

Answer 1

The correct option is A $1$

${\cos }^2{73}^{\circ }+{\cos }^2{47}^{\circ }-{\sin }^2{43}^{\circ }+{\sin }^2{107}^{\circ }$

$={\cos }^2{47}^{\circ }-{\sin }^2{43}^{\circ }+{\cos }^2{73}^{\circ }+{\sin }^2{107}^{\circ }$

$={\cos }^2{47}^{\circ }-{\cos }^2\left({90}^{\circ }-{43}^{\circ }\right)+{\cos }^2{73}^{\circ }+{\sin }^2\left({180}^{\circ }-{73}^{\circ }\right)$

$={\cos }^2{47}^{\circ }-{\cos }^2{47}^{\circ }+{\cos }^2{73}^{\circ }+{\sin }^2{73}^{\circ }$

$=1$ (since ${\sin }^{2}x+{\cos }^{2}x=1$)