In a right angle triangle ABC, where ∠B = 90°, if tan A = 1, then find the value of 4 sin A cos A.

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Given that ∠B = 90°, triangle ABC is a right triangle with B as the right angle.

Given tan A = 1.
Recall that tan A = opposite/adjacent.
If tan A = 1, then opposite side = adjacent side.

Let the opposite side = adjacent side = 1 unit.
Then hypotenuse = √(1^2 + 1^2) = √2.

Now, sin A = opposite/hypotenuse = 1/√2 = √2/2.
cos A = adjacent/hypotenuse = 1/√2 = √2/2.

Calculate 4 sin A cos A:
= 4 × (√2/2) × (√2/2)
= 4 × (2/4)
= 4 × 1/2
= 2.

Therefore, the value of 4 sin A cos A is 2.

Answer

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