Question

For any acute angle $\theta$, find ${\sin }^2\theta +{\cos }^2\theta$

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is A $1$

Consider right angled $△ABC$, where $\angle B={90}^{\circ }$ and $\angle A=\theta$.

Let $AB=x,BC=y$ and $AC=r$

So, by Pythagoras theorem, $x^2+y^2=r^2$

${\sin }^2\theta +{\cos }^2\theta ={\left(\frac{y}{r}\right)}^2+{\left(\frac{x}{r}\right)}^2=\frac{y^2}{r^2}+\frac{x^2}{r^2}=\frac{x^2+y^2}{r^2}=\frac{r^2}{r^2}=1$

So, $1$ is correct.