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
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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