Question

If θ is an acute angle and sin θ = cos θ, find the value of 2 tan² θ + sin² θ – 1.

Answer 1

sin θ = cos θ

`\Rightarrow \frac{\sin \theta }{\cos \theta }=\frac{\cos \theta }{\cos\theta }`   ...[Dividing both sides by cos θ]

⇒ tan θ = 1

⇒ tan θ = tan 45° 

⇒ θ = 45°

∴ 2 tan² θ + sin² θ – 1

= 2 tan² 45° + sin² 45° – 1

= `2 xx (1)^{2} + (\frac{1}{\sqrt{2}} )^{2} - 1`

= `2 + \frac{1}{2} - 1`

= `1 + \frac{1}{2}`

= `\frac{2 + 1}{2}`

= `\frac{3}{2}`