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]

⇒ tanθ = 1

⇒ tanθ = tan45° ⇒ θ= 45°

`∴ 2 tan^2 θ + sin^2 θ – 1`

`= 2tan^2 45° + sin^2 45° – 1`

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

`=2+\frac{1}{2}-1=\frac{5}{2}-1=\frac{3}{2}`