Question

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

• A. $1$
• B. $\frac{1}{2}$
• C. $\frac{\sqrt{3}}{2}$
• D. ${\sin }^2{73}^{\circ }+{\sin }^2{47}^{\circ }$

Answer 1

The correct option is A $1$

Consider the given equation.

$co{s}^2{73}^0+co{s}^2{47}^0-si{n}^2{43}^0+si{n}^2{107}^0$

$\Rightarrow co{s}^2{73}^0+co{s}^2{47}^0-si{n}^2({90}^0-{47}^0)+si{n}^2({180}^0-{73}^0)$

$\Rightarrow (co{s}^2{73}^0+{\sin }^2{73}^0)+co{s}^2{47}^0-{\cos }^2{47}^0$

$\Rightarrow 1$

Hence, this is the answer.