Grade 11Trigonometry
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
1 Answer
Arun
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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