cos2A[3-4cos2A]2+sin2A[3-4sin2A]2=
cos4A
sin4A
1
None of these.
Simplify the series using Trigonometric identity:
cos2A[3-4cos2A]2+sin2A[3-4sin2A]2={cosA(3-4cos2A)}2+{sinA(3-4sin2A)}2={3cosA-4cos3A}2+{3sinA-4sin3A}2={cos3A}2+{sin3A}2{∵cos3A=4cos3A-3cosA,sin3A=3sinA-4sin3A}=cos23A+sin23A{∵cos2A+sin2A=1)=1
Therefore, Option (C) is the correct answer.