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paradox xyz cool Grade: 11
        

prove that


tanA + 2tan2A + 4tan4A + 8cot8A = cotA

6 years ago

Answers : (2)

AKASH GOYAL AskiitiansExpert-IITD
419 Points
										

Dear Paradox


Solving from right
tan 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/tan4A

Proceeding as above, we will reach to
tan A + 2tan2A + 4tan4A + 8cot8A = 1/tanA = cotA
Hence proved.


All the best.


AKASH GOYAL


AskiitiansExpert-IITD


 


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6 years ago
vikas askiitian expert
510 Points
										

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


 

6 years ago
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