2014 · Q65
If sin x + cos x = p and sin³x + cos³x = q, then what is p³ − 3p equal to?
Elementary MathematicsTrigonometry
- A0
- B−2q
- C2q
- D4q
Explanation
p³ = q + 3p sin x cos x and q = p(1 − sin x cos x); eliminating sin x cos x gives p³ = 3p − 2q.
If sin x + cos x = p and sin³x + cos³x = q, then what is p³ − 3p equal to?
Explanation
p³ = q + 3p sin x cos x and q = p(1 − sin x cos x); eliminating sin x cos x gives p³ = 3p − 2q.