Question

For acute angle $\theta$, find value of ${\sec }^2\theta -{\tan }^2\theta$

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is A $1$

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

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

By Pythagoras theorem, $x^2+y^2=r^2$

${\sec }^2\theta -{\tan }^2\theta ={\left(\frac{r}{x}\right)}^2={\left(\frac{y}{x}\right)}^2=\frac{r^2}{x^2}-\frac{y^2}{x^2}=\frac{r^2-y^2}{x^2}=\frac{x^2}{x^2}=1$

So, $1$ is correct.