Question

1 - 8 cos²α + 8 cos⁴α = ?

a) cos 4α
b) 4cos α
c) sin 4α
d) cos 4α​

Answer 1

1 - 8 cos²α + 8 cos^4 α

= 1 – 8 cos²α ( 1 – cos²α )

= 1 – 8 cos²α sin²α

= 1 – 2 × ( 2sinαcosα)²

= 1 – 2 sin² 2α

= cos 2 (2α) [ as cos 2x = 1 – 2 sin²x]

= cos 4α