1.

What is the value of (1 + tan42°)(1 + tan3°)?1. 22. 13. 34. –2

Answer» Correct Answer - Option 1 : 2

GIVEN:

X = (1 + tan42°)(1 + tan3°)

FORMULA:

If A = B + C

tan A = tan(B + C) = (tan B + tan C)/(1 – tan B tan C)

⇒ tan A = (tan B + tan C)/(1 – tan B tan C)

⇒ tan A – tan A tan B tan C = tan B + tan C

⇒ tan A = tan B + tan C + tan A tan B tan C

CALCULATION:

X = (1 + tan42°)(1 + tan3°)

⇒ X = 1 + tan42° + tan3° + tan42°tan3°

⇒ X = 1 + (tan42° + tan3° + tan42°tan3°)

⇒ X = 1 + (tan42° + tan3° + tan45°tan42°tan3°)

⇒ X = 1 + tan45°

⇒ X = 1 + 1

⇒ X = 2


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