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Prove that tanA+2tan2A+4cot4A=cotA

Prove that tanA+2tan2A+4cot4A=cotA

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Pradhan,

 

Start this problem from the right end of the LHS

 

2tan2A+4cot4A = 2tan2A+4/tan4A = 2tan2A + 2(1-tan22A)/(tan2A) = 2/tan2A

So tanA+2tan2A+4cot4A = tanA + 2/tan2A = tanA + (1-tan2A)/tanA = 1/tanA = cotA.

 

Best Regards,

Ashwin (IIT Madras).

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