In a right angle △ ABC , ∠ B = 90° , if tanA = 1, then 4 sinA cosA =_____.

In a right angle △ ABC , ∠ B = 90° , if tanA = 1, then 4…

In a right angle $\triangle ABC$ , $\angle B = 90°$ , if tanA = 1, then 4 sinA cosA =_________________.

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 2.

In ΔABC, ∠B = 90°, tanA = Perpendicular/Base = 1

So, ΔABC is an isosceles right angle triangle.

Let BC = AB = k

By Pythagorean theorem, AC² = AB² + BC² = k² + k² = 2k²

⇒ AC = √(2k²) = k√2

Now, 4sinAcosA = 4(1/√2)(1/√2) = 4(1/2) = 2

Therefore, the value of 4sinAcosA is 2.