Correct Answer - Option 3 : (2√2 – 1)/√2
Given:
A + B = 45°
Concept used:
1.) cos(A + B) = cosAcosB – sinAsinB
2.) If A + B = 45° then (1 + tanA)(1 + tanB)
Calculations:
sinASinB + (1 + tanA)(1 + tanB) – cosAcosB
⇒ (1 + tanA)(1 + tanB) – cosAcosB + sinAsinB
⇒ (1 + tanA)(1 + tanB) – (cosAcosB – sinAsinB)
⇒ (1 + tanA)(1 + tanB) – cos(A + B)
Here A + B = 45°
⇒ 2 – cos(45°)
⇒ 2 – 1/√2
⇒ (2√2 – 1)/√2
∴ The correct answer is (2√2 – 1)/√2