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If A + B = 45° then find the value of sinASinB + (1 + tanA)(1 + tanB) – cosAcosB
1. (2√2 – 1)/2
2. (2√2 + 1)/2
3. (2√2 – 1)/√2
4. (2√2 + 1)/√2

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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

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