Question

show that the expression of COS 4A in term of COS A is 8COS^4A - 8COS^A +1
sofia sis I choose truth so go ahead​

Answer 1

Question :—

Prove that : cos 4A = 8cos⁴A −8cos²A+1

Answer :—

L.H.S = cos 4A = cos 2(2A)

= 2cos²2A−1

= 2(2cos²A−1)² −1

= 2(4cos⁴A+1−4cos²A)−1

= 8cos⁴A+2−8cos²A−1

= 8cos⁴A−8cos²A+1 = R.H.S

Hence proved.

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Answer 2

Answer:

Question :—

Prove that : cos 4A = 8cos⁴A −8cos²A+1

Answer :—

L.H.S = cos 4A = cos 2(2A)

= 2cos²2A−1

= 2(2cos²A−1)² −1

= 2(4cos⁴A+1−4cos²A)−1

= 8cos⁴A+2−8cos²A−1

= 8cos⁴A−8cos²A+1 = R.H.S

Hence proved.