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How to integrate ∫(cos2x-cos2a)/(cosx-cosa)dx where a is constant

How to integrate ∫(cos2x-cos2a)/(cosx-cosa)dx where a is constant

Grade:12

3 Answers

Arun
25750 Points
6 years ago
∫(cos 2x - cos 2a) / (cos x - cos a) dx 
= ∫((2cos^2 x - 1) - (2cos^2 a - 1)) / (cos x - cos a) dx 
= ∫(2 cos^2 x - 2 cos^2 a) / (cos x - cos a) dx 
= ∫[2(cos x - cos a)(cos x + cos a)] / (cos x - cos a) dx 
= ∫2(cos x + cos a) dx 
= 2 sin x + x cos a + c.
Rakshit Puri
15 Points
5 years ago
Hsbs
 
∫(cos 2x - cos 2a) / (cos x - cos a) dx 
= ∫((2cos^2 x - 1) - (2cos^2 a - 1)) / (cos x - cos a) dx 
= ∫(2 cos^2 x - 2 cos^2 a) / (cos x - cos a) dx 
= ∫[2(cos x - cos a)(cos x + cos a)] / (cos x - cos a) dx 
= ∫2(cos x + cos a) dx 
= 2 sin x + 2x cos a + c
ankit singh
askIITians Faculty 614 Points
3 years ago
= 2 sin x + 2x cos a + c= ∫2(cos x + cos a) dx = ∫[2(cos x - cos a)(cos x + cos a)] / (cos x - cos a) dx = ∫(2 cos^2 x - 2 cos^2 a) / (cos x - cos a) dx ∫((2cos^2 x - 1) - (2cos^2 a - 1)) / (cos x - cos a) dx 

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