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If tanθ = 3/4 then find the value of sin2(90° + θ) + tan2θ – cos2(90° + θ).
1. 333/400
2. 331/400
3. 337/400
4. 323/400

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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 

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