Question

If $\alpha$ and $\beta$ complementary angles then ${\sin }^2({90}^o-\alpha )+{\sin }^2({90}^o-\beta )=$

• A. $0$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

The correct option is B $1$

$\alpha +\beta ={90}^o\Rightarrow \alpha ={90}^o-\beta$

Now, ${\sin }^2({90}^o-\alpha )+{\sin }^2({90}^o-\beta )={\sin }^2({90}^o-\alpha )+{\sin }^2\alpha ={\cos }^2\alpha +{\sin }^2\alpha =1$

Therefore, Answer is $1$