Find the value of 2 tan2 θ + sin2 θ – 1.

If θ is an acute angle and sin θ = cos θ, find the value of θ and hence, find the value of 2 tan² θ + sin² θ – 1.

Answer :

sin θ = cos θ

sin θ/cos θ = 1

tan θ = 1

tan 45° = 1

tan θ = tan 45°

θ = 45°

2 tan² θ + sin² θ – 1 = 2 tan² 45° + sin² 45° – 1

= 2 (1)² + (1/√2)² – 1

= (2×1×1) + ½ – 1

= 2 + ½ – 1

= 5/2 – 1

= (5 – 2)/2

= 3/2

Hence, 2 tan² θ + sin² θ – 1 = 3/2.

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