prove the following

Asked by sunil_0010 | 1st Nov, 2009, 04:03: PM

Expert Answer:

(cos8θ-sin8θ) = (cos4θ-sin4θ)(cos4θ+sin4θ)

= (cos2θ-sin2θ)(cos2θ+sin2θ)(cos4θ+sin4θ)

= (cos2θ-sin2θ)(cos4θ+sin4θ)

= (cos2θ-sin2θ)(cos4θ+sin4θ)..............(1)

Now (cos2θ+sin2θ)2 =cos4θ+ 2sin2θcos2θ + sin4θ

1 = cos4θ+ 2sin2θcos2θ + sin4θ

cos4θ+sin4θ = 1 - 2sin2θcos2θ.............using this result in (1).

(cos8θ-sin8θ) = (cos2θ-sin2θ)(1 - 2sin2θcos2θ)

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Answered by  | 1st Nov, 2009, 10:42: PM

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