Question

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

(A) 1/2

(B) 3/2

(C) 5/2

(D) 7/2

Answer 1

The correct answer is (B) 3/2

We have,

sin θ = cos θ

sin θ/ cos θ = cos θ/ cos θ  [ Dividing both sides by cos θ]

tan θ = 1

tan θ = tan 45°

θ = 45°

2 tan² θ + sin² θ – 1

= 2 tan² 45° + sin²45° - 1

= 2 (1)² + (1/√2)² – 1

= 2 + 1/2 – 1

= (4 + 1 – 2)/2

= 3/2