In a right triangle ABC, right-angled at B, if tan A = 2, what is the value of 2 sin A cos A?
Show answer & explanation
Correct answer: A
Explanation
tan A = 2
According to the formula:
tan A = sin A / cos A
2 sin A cos A = sin 2A
tan A = 2 = sin A / cos A
assume
sin A = 2k, cos A = k
sin²A + cos²A = 1
(2k)² + k² = 1
4k² + k² = 1
5k² = 1
k = 1/√5
sin A = 2/√5
cos A = 1/√5
2 sin A cos A= 2 × (2/√5) × (1/√5)= 4/5