Question

(2cosA+1)(2cosA-1)(2cos2A-1)(2cos4A-1)=2cos8A+1 prove that​

Answer 1

Proof:

L.H.S. = (2 cosA + 1) (2 cosA - 1) (2 cos2A - 1) (2 cos4A - 1)

= {(2 cosA + 1) (2 cosA - 1)} (2 cos2A - 1) (2 cos4A - 1)

= (4 cos²A - 1) (2 cos2A - 1) (2 cos4A - 1)

= {2 (2 cos²A - 1) + 1} (2 cos2A - 1) (2 cos4A - 1)

= (2 cos2A + 1) (2 cos2A - 1) (2 cos4A - 1)

= {(2 cos2A + 1) (2 cos2A - 1)} (2 cos4A - 1)

= (4 cos²2A - 1) (2 cos4A - 1)

= {2 (2 cos²2A - 1) + 1} (2 cos4A - 1)

= (2 cos4A + 1) (2 cos4A - 1)

= 4 cos²4A - 1

= 2 (2 cos²4A - 1) + 1

= 2 cos8A + 1 = R.H.S.

Hence, proved.

Trigonometric Rules:

• 2 cos²A - 1 = cos2A
• 2 cos²2A - 1 = cos4A
• 2 cos²4A - 1 = cos8A

Answer 2

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Answer: