Grade 11Trigonometry
The value of tan(pi/12) + 2tan(2 pi/12) + 4tan(4 pi/12) + 8cot(8 pi/12) ,is. Ans: cot (pi /12)
The value of tan(pi/12) + 2tan(2 pi/12) + 4tan(4 pi/12) +
8cot(8 pi/12) ,is. Ans: cot (pi /12)
4 Answers
Arun
Approved Tutor Answer7 Years agoDear student
I want you to remember this-
tan A + 2 tan 2A + 4 tan4A + 8cot 8A = cot A
Hence for the above question, A = pi/12
Hence answer will be cot pi/12
Heisenberg
But sir can you prove that part where you said that the result is important?
remembering so many formulae plus so many results is a had job......
Arun
Dear student
I am giving you some hint you can solve this then,
take 8 cot 8A now open this in the form of tan 4A
after this you will clearly find ome common in terms one by one from right to left. and final result will be cot A
Aditya Gupta
heisenberg an even better way to solve is to use the identity tanx= cotx – 2cot2x
note that the rth term of summation is 2^(r-1)tan(2^(r-1)y) where y is pi/12.
write it as 2^(r-1)[cot(2^(r-1)y) – 2cot2^ry]
= 2^(r-1)cot(2^(r-1)y) – 2^rcot2^ry, which is easily seen to telescope!
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