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Prove that: Tan alpha+ 2 tan 2alpha + 4 tan 4alpha +8 cot 8alpha= cot alpha

Prove that:  Tan alpha+ 2 tan 2alpha + 4 tan 4alpha +8 cot 8alpha= cot alpha

Grade:11

1 Answers

Arun
25763 Points
3 years ago
consider
tan A – cot A  – 2 tan 2A
 
we know that
 
cot A –  tan A = cos^2 A – sin^2 A / sinA cos A = 2 cot 2A
 
2 cot 2A –  2 tan 2A
 
2 (cot 2A –  tan 2A)
 
 = 4 cot 4A
 
similarly
 
cot A – tanA – 2 tanA – 4 tan4A
 
4 (cot 4A – tan4A)
 
8 cot 8A
 
i.e.
 
cot A – tanA – 2 tan2A – 4 tan 4A = 8 cot 8A
 
 tanA + 2 tan2A + 4 tan 4A + 8 cot 8A = cot A
 
Hence proved

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