In a triangle ABC right-angled at C, if tan A = √3, then find the value of sinA × cosB × cot(A + B).

Question

Accepted Answer

Given triangle ABC is right-angled at C, so angle C = 90°. Therefore, A + B = 90°.

Given tan A = √3.

Recall that tan 60° = √3, so A = 60°.

Since A + B = 90°, B = 30°.

Calculate each term:
- sin A = sin 60° = √3/2
- cos B = cos 30° = √3/2
- cot(A + B) = cot 90° = cot 90° = 0 (cot 90° = 0)

However, cot 90° is 0, so the product sinA × cosB × cot(A + B) = (√3/2) × (√3/2) × 0 = 0.

But this contradicts the options and the initial assumption. Let's re-examine cot(A + B).

Since A + B = 90°, cot 90° = 0.

Therefore, the product is 0.

But option 3 is 0, which matches the calculation.

Rechecking the problem statement and options, option 3 is 0.

Hence, the correct answer is 0.

Answer

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