Question

e) Which one of the following is true i.e., cos4a= ? Your options are as follows:
18sin²acos²a - 1 ii) 1 - 8sin²acos²a ii)Both (1) and (ii) are true. iv)None of these. Give your answer
with a convenient proof.​

Answer 1

Answer:

First 5 natural numbers in form ( 3n + 2 ) are = 5 , 8 , 11 , 14 , 17

Cubes of these numbers are,

= 53 = 5 × 5 × 5 = 125

= 83 = 8 × 8 × 8 = 512

= 113 = 11 × 11 × 11 = 1331

= 143 = 14 × 14 × 14 = 2744

= 173 = 17 × 17 × 17 = 4313

We find that all these cubes give remainder 2 when divided by 3..

Hence statement is true.

Answer 2

Cos4a = 1 - 8sin²acos²a

Refer the attachment ^_^