2012 · Q65
If p = a sin x + b cos x and q = a cos x - b sin x, then what is p^2 + q^2 equal to?
Elementary MathematicsTrigonometry
- Aa + b
- Bab
- Ca^2 + b^2
- Da^2 - b^2
Explanation
Expanding, the cross terms cancel and p^2+q^2 = a^2(sin^2x+cos^2x) + b^2(cos^2x+sin^2x) = a^2+b^2.