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Prove that : Cos3 theta + 2cos5 theta + cos7 theta / costheta + 2cos3 theta + cos 5 theta= cos 2 theta - sin2 theta*tan3 theta

Prove that   :     Cos3 theta + 2cos5 theta +  cos7 theta / costheta + 2cos3 theta + cos 5 theta= cos 2 theta - sin2 theta*tan3 theta

Grade:11

1 Answers

Arun
25757 Points
4 years ago
Numerator Part
 
cos 3a + 2 cos 5a + cos 7a = 2 cos 5a cos 2a + 2 cos 5a
 
Denominator Part
 
cos a + 2 cos 3a + cos 5a = 2 cos 3a  cos 2a + 2 cos 3a
 
Now
 
it becomes 
 
2 cos 5a (1 + cos 2a) / 2 cos 3a (1 + cos 2a) = cos 5a / cos 3a
 
 = cos (3a + 2a) / cos 3a
 
 = cos 3a cos 2a /  cos 3a   –  sin3a sin 2a / cos 3a
 
 = cos 2a – sin2a tan 3a
 
hope it helps
 
Regards
Arun (askIITians forum expert)

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