Brooklyn Santiago

2023-03-11

If $\theta$ is an acute angle and $\mathrm{sin}\theta =\mathrm{cos}\theta$. The value of $2{\mathrm{tan}}^{2}\theta +{\mathrm{sin}}^{2}\theta -1$ is,

### Answer & Explanation

ecchieuz

$⇒$$\frac{\mathrm{sin}\theta }{\mathrm{cos}\theta }=\frac{\mathrm{cos}\theta }{\mathrm{cos}\theta }$
$⇒$$\mathrm{tan}\theta =\frac{\mathrm{sin}\theta }{\mathrm{cos}\theta }$
$⇒$$\mathrm{tan}\theta =1$
$⇒$$\mathrm{tan}\theta =\mathrm{tan}45°$
$⇒$$\theta =45°$
$⇒$$2{\mathrm{tan}}^{2}\theta +{\mathrm{sin}}^{2}\theta -1=2{\mathrm{tan}}^{2}45°+{\mathrm{sin}}^{2}45°-1$
$=2{\left(1\right)}^{2}+{\left(\frac{1}{2}\right)}^{2}-1$
$=\frac{3}{2}$(answer)

Do you have a similar question?

Recalculate according to your conditions!