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prove that tanA + 2tan2A + 4tan4A + 8cot8A = cotA prove that tanA + 2tan2A + 4tan4A + 8cot8A = cotA
prove that
tanA + 2tan2A + 4tan4A + 8cot8A = cotA
Dear Paradox Solving from righttan A + 2tan2A + 4tan4A + 8cot8A = tan A + 2tan2A + 4tan4A + 8/tan8A = tan A + 2tan2A + 4tan4A + 8(1-tan24A)/2tan4A = tan A + 2tan2A + [{4tan4A(tan4A)} + 4 (1-tan24A)]/tan4A = tan A + 2tan2A + [4tan24A + 4 - tan24A]/tan4A = tan A + 2tan2A + 4/tan4AProceeding as above, we will reach totan A + 2tan2A + 4tan4A + 8cot8A = 1/tanA = cotAHence proved. All the best. AKASH GOYAL AskiitiansExpert-IITD Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..
Dear Paradox
Solving from righttan A + 2tan2A + 4tan4A + 8cot8A = tan A + 2tan2A + 4tan4A + 8/tan8A = tan A + 2tan2A + 4tan4A + 8(1-tan24A)/2tan4A = tan A + 2tan2A + [{4tan4A(tan4A)} + 4 (1-tan24A)]/tan4A = tan A + 2tan2A + [4tan24A + 4 - tan24A]/tan4A = tan A + 2tan2A + 4/tan4AProceeding as above, we will reach totan A + 2tan2A + 4tan4A + 8cot8A = 1/tanA = cotAHence proved.
All the best.
AKASH GOYAL
AskiitiansExpert-IITD
Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.
Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.
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TANA + 2TAN2A + 4TAN4A + 8COT8A = COTA .........1 WE HAVE FORMULA , COTA-TANA=2COT2A EQ 1 CAN BE WRITTEN AS 2TAN2A + 4TAN4A + 8COT8A = COTA-TANA 2TAN2A + 4TAN4A + 8COT8A = 2COT2A ( BY USING FORMULA ) 4TAN4A + 8COT8A = 2COT2A - 2TAN2A 4TAN4A + 8COT8A =4COT4A (BY USING FORMULA) 8COT8A = 4COT4A - 4TAN4A =8COT8A (BY USING FORMULA ) HENCE PROVED
TANA + 2TAN2A + 4TAN4A + 8COT8A = COTA .........1
WE HAVE FORMULA , COTA-TANA=2COT2A
EQ 1 CAN BE WRITTEN AS
2TAN2A + 4TAN4A + 8COT8A = COTA-TANA
2TAN2A + 4TAN4A + 8COT8A = 2COT2A ( BY USING FORMULA )
4TAN4A + 8COT8A = 2COT2A - 2TAN2A
4TAN4A + 8COT8A =4COT4A (BY USING FORMULA)
8COT8A = 4COT4A - 4TAN4A
=8COT8A (BY USING FORMULA )
HENCE PROVED
Dear Student,Please find below the solution to your problem.Solving from righttan A + 2tan2A + 4tan4A + 8cot8A= tan A + 2tan2A + 4tan4A+ 8/tan8A= tan A + 2tan2A + 4tan4A + 8(1-tan24A)/2tan4A= tan A + 2tan2A + [{4tan4A(tan4A)} + 4 (1-tan24A)]/tan4A= tan A + 2tan2A + [4tan24A + 4 - tan24A]/tan4A= tan A + 2tan2A + 4/tan4AProceeding as above, we will reach totan A + 2tan2A + 4tan4A + 8cot8A = 1/tanA = cotAThanks and Regards
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