Question

Prove that: tan a + 2 tan 2a + 4 tan 4a + 8 cot 8a = cota.
​

Answer 1

Answer:

first of all, we find one important results.

cot A-tan A

=

1

tan A

1 - tan² A

tan A

2(1 - tan² A)

2tan A

= 2cot2 A

- tan A

41%

=

hence,

cotA - tanA = 2cot2A

cotA= 2cot2A + tanA use this

application here,

SO,

tanA + 2tan2A + 4{tan4A +2cot8A}

= tanA + 2tan2A + 4cot4A by using

above application

tanA + 2{tan2A + 2cot4A}

=

= tanA + 2cot2A by using above

application

=cotA by using above application

hence,

tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A =

cotA

Answer 2

Answer:

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