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Prove sin(n+1)a-sin(n-1)a/cos(n+1)a+cos2a+cos(n-1)a=tan a/2

Prove sin(n+1)a-sin(n-1)a/cos(n+1)a+cos2a+cos(n-1)a=tan a/2

Grade:11

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
7 years ago
Solution:This can be simplified as follows:
sin(n+1)a-sin(n-1)a=2cos(na)sin(a) and cos(n+1)a+cos(n-1)a+cos(2a)=2cos(na)cos(a)+2cos^{2}(a)-1
After this, the substitution for cos(a) should be done as follows:
cos(a)=\frac{1-tan^{2}(a/2))}{1+tan^{2}(a/2)}
Substitituting this, the cos(na) factor gets cancelled.
Thanks & Regards
Sumit Majumdar,
askIITians Faculty
Ph.D,IIT Delhi

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