Trigonometric series
If we have cosine series in its product form where angles are in G.P. with the common ratio 2 then multiply both the numerator and denominator by 2 sin (least angle).
Illustration: Simplify product cosA cos2A×cos22A .... Cos2n-1A.
Solution: cosA× cos2A....cos2n-1A = 1/2sinA (sin2A.cos2A)×cos2A....cos2n-1A
= 1/2sinA× (sin2A. cos2A)......cos2n-1A = 1/22 sinA (sin2A. cos2A) ......cos2n-1A
Continue like this, finally we have =
Note:
- where ∏ denotes products .
- If we have a cosine series or a sine series in its sum form where angles are in A.P. then multiply numerator and denominator both with 2sin( common diffrence/2) .
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