If θ is an acute angle and sin θ = cos θ, then the value of $2 tan^2 θ + sin^2 θ - 1 $ is equal to :
Answer & explanation
Correct answer: option 4
sinθ = cosθ
{ we know, sinA = cosB Iff A + B = 90º }
So, θ + θ= 90º
θ= 45º
Now,
2tan²θ + sin²θ - 1
= 2tan²45º + sin²45º - 1
= 2 + ( \(\frac{1}{√2}\) )² - 1
= 2 + \(\frac{1}{2}\) - 1
= \(\frac{3}{2}\)