Trigonometric EquationMedium
Question
If sin x + sin2 x = 1, then cos12x + 3cos10 x + 3cos8x + cos6x - 2 is equals to -
Options
A.0
B.1
C.-1
D.2
Solution
sin x = 1 - sin2x = cos2x
⇒ Now sin6x + 3sin5x + 3sin4x + sin3x - 2
= (sin2x)3 + 3(sin2x)2 sinx + 3(sin2x)2 + sin2x sinx -2
= (sin2x + sinx)3 -2 = 1 -2 = -1
⇒ Now sin6x + 3sin5x + 3sin4x + sin3x - 2
= (sin2x)3 + 3(sin2x)2 sinx + 3(sin2x)2 + sin2x sinx -2
= (sin2x + sinx)3 -2 = 1 -2 = -1
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