Mark the Correct alternative in the following:
The value of 2 cos x – cos 3x – cos 5x – 16 cos3 x sin2 x is
Given expression is 2 cos x – cos 3x – cos 5x – 16 cos3 x sin2 x
Consider the expression
2 cos x – cos 3x – cos 5x – 16 cos3 x sin2
= 2 cos x – (cos 5x + cos 3x) – 16 cos3 x sin2 x
[using the sum of angles 
]
= 2 cos x – [2 cos 4x cos x] - 16cos3 x sin2 x
= 2 cos x (1 – cos 4x ) - 16cos3 x sin2 x
[ using the property cos 2θ = 1- 2 sin2 θ ]
= 2 cos x [ 1 – (1 – 2 sin2 2x)] -16cos3 x sin2 x
= 2 cos x [2 sin2 2x] -16cos3 x sin2 x
= 4cos x [2sin x cos x]2 -16cos3 x sin2 x
[ using sin 2θ = 2 sin θ cos θ ]
= 4 × 4 (cos x sin2 x cos2 x) -16cos3 x sin2 x
= 16cos3 x sin2 x -16cos3 x sin2 x
= 0
Hence cos x – cos 3x – cos 5x – 16 cos3 x sin2 x = 0
The answer is option C.