If tanθ = 4/3, find cos²θ - sin²θ.
Show answer & explanation
Correct answer: D
Explanation
Given:
tanθ = 4/3
By the formula:
cos²θ − sin²θ = (1 − tan²θ) / (1 + tan²θ)
tan²θ = (4/3)² = 16/9
cos²θ − sin²θ
= (1 − 16/9) / (1 + 16/9)
= (9/9 − 16/9) / (9/9 + 16/9)
= (−7/9) / (25/9)
= −7/25