Correct Answer - Option 3 : 337/400
Given:
tanθ = 3/4
Concept used:
1.) tanθ = P/B
2.) sinθ = P/H
3.) cosθ = B/H
4.) Pythagoras Theorem
H2 = P2 + B2
5.) sin(90° + θ) = cosθ
6.) Cos(90° + θ) = -sinθ
Where,
P → Perpendicular
B → Base
H → Hypotenus
Calculations:
tanθ = 3/4 = P/B
H2 = P2 + B2
⇒ H2 = (3)2 + (4)2
⇒ H = √25 = 5
sinθ = 3/5
cosθ = 4/5
sin2(90° + θ) + tan2θ – cos2(90° + θ)
⇒ cos2θ + tan2θ – (-sinθ)2
⇒ cos2θ + tan2θ – sin2θ
⇒ (4/5)2 + (3/4)2 – (3/5)2
⇒ 16/25 + 9/16 – 9/25
⇒ (256 + 225 – 144)/400
⇒ 337/400
∴ The correct answer is 337/400