Question

Prove - tan theta + 2tan2theta + 4tan4theta + 8cot8theta = cot theta

Answer 1

To prove - tan Ф + 2 tan 2Ф + 4 tan 4Ф + 8 cot 8Ф = cot Ф

Simply bring all the elements on L.H.S to R.H.S and equate it to zero.

Refer the solution given below -

cot Ф - tan Ф - 2 tan 2Ф - 4 tan 4Ф - 8 cot 8Ф

We know that ,
cot Ф - tan Ф = 2 cot 2Ф

Applying the important deduction,

= (cot Ф - tan Ф) - 2 tan 2Ф - 4 tan 4Ф - 8 cot 8Ф
= 2 cot 2Ф - 2 tan 2Ф - 4 tan 4Ф - 8 cot 8Ф
= 2( cot 2Ф - tan 2Ф) - 4 tan 4Ф - 8 cot 8Ф
= 2(2 cot 4Ф) - 4 tan 4Ф - 8 cot 8Ф
= 4 cot 4Ф - 4 tan 4Ф - 8 cot 8Ф
= 4(cot 4Ф - tan 4Ф) - 8 cot 8Ф
= 4(2 cot 8Ф) - 8 cot 8Ф
= 8 cot 8Ф - 8 cot 8Ф
= 0 = R.H.S

Hope This Helps You!

Answer 2

Answer:

Step-by-step explanation:

This question need basic formula which l wrote in image.....

And need lots of patience...

It might help u