2019 · Q32
If cos²x + cos x = 1, then what is the value of sin¹²x + 3sin¹⁰x + 3sin⁸x + sin⁶x?
Elementary MathematicsTrigonometry
- A1
- B2
- C4
- D8
Explanation
From cos^2x+cosx = 1, sin^2x = 1-cos^2x = cosx. The expression becomes cos^6x+3cos^5x+3cos^4x+cos^3x = cos^3x(cosx+1)^3 = [cosx(cosx+1)]^3. But cosx(cosx+1) = cos^2x+cosx = 1, so the value is 1.