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

1.	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» 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

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»

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