In a right triangle ABC, right-angled at B, if tan A = 1, what is the value of 2sinAcos A?
Show answer & explanation
Correct answer: D
Explanation
In right triangle ABC, ∠B = 90°
tan A = 1
tan A = sin A / cos A
sin²A + cos²A = 1
2 sin A cos A = sin 2A
tan A = 1 ⇒ sin A = cos A
sin A = cos A = k
k² + k² = 1
2k² = 1
k² = 1/2
sin A = cos A = 1/√2
2 sin A cos A = 2 × (1/√2) × (1/√2)= 1