Question

lf sin θ = cos θ, then the value of 2 tan² θ + sin² θ – 1 is equal to ______.

Options

• `1/2`

• `5/2`

• `3/2`

• 2

Answer 1

lf sin θ = cos θ, then the value of 2 tan² θ + sin² θ – 1 is equal to `underlinebb(3/2)`.

Explanation:

sin θ = cos θ

`\implies sinθ/cosθ` = 1

`\implies` tan θ = 1

`\implies` θ = 45°

∴ 2 tan² θ + sin² θ – 1 = 2 tan² 45° + sin² 45° – 1

= `2(1)^2 + (1/sqrt(2))^2 - 1`

= `2 + 1/2 - 1`

= `3/2`