Question

If sin θ = cos θ , then 2 tan²θ + sin²θ – 1 is equal to

Options

• `(-3)/2`

• `3/2`

• `2/3`

• `(-2)/3`

Answer 1

`3/2`

Explanation;

Hint:

sin θ = cos θ

`sin theta/cos theta` = 1 

⇒ tan θ = 1

AC = `sqrt("AB"^2 + "BC"^2)`

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

= `sqrt(2)`

sin θ = `1/sqrt(2)`

2 tan²θ + sin²θ − 1 = `2(1)^2 + (1/sqrt(2))^2 - 1`

= `2 + 1/2 - 1`

= `(4 + 1 - 2)/2`

= `(5 - 2)/2`

= `3/2`