If sin A = 3/5, and A is acute, find the value of sec² A - tan² A.
Show answer & explanation
Correct answer: D
Explanation
Given:
sin A = 3/5, A is an acute angle.
By the formula:
sin²A + cos²A = 1
tanA = sinA / cosA
secA = 1 / cosA
sinA = 3/5
cosA = √(1 − sin²A)
= √(1 − 9/25)
= √(16/25)
= 4/5
tanA = (3/5) / (4/5) = 3/4
secA = 1 / (4/5) = 5/4
sec²A − tan²A = (5/4)² − (3/4)²
= 25/16 − 9/16
= 16/16
= 1