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Question

If tan A = 1 and tan B = √ 3, what is the value of cos A . cos B - sin A . sin B?

A (1 + √3)/2√2 Correct Answer Incorrect Answer
B (1 - √3)/2√2 Correct Answer Incorrect Answer
C 2√2/3 Correct Answer Incorrect Answer
D 1 Correct Answer Incorrect Answer

Solution

Given, tan A = 1 ⇒ A = 45° Also given, tan B = √ 3 ⇒ B = 60° ∴ cos A . cos B - sin A . sin B = cos 45° . cos 60° - sin 45° . sin 60° = 1/ √ 2 * 1/2 - 1/ √ 2 . √ 3/2 = (1 - √ 3)/2 √ 2

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