If tan &#x2061;<!-- ⁡ --> x + tan 2 </msup> &#x2061;<!-- ⁡ --> x

Lena Bell 2022-07-03 Answered
If tan x + tan 2 x + tan 3 x = 1 then we have to find the value of 2 cos 6 x 2 cos 4 x + cos 2 x
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Answers (2)

Alexis Fields
Answered 2022-07-04 Author has 14 answers
The condition gives
( tan x + 1 ) ( tan 2 x + 1 ) = 2
or
2 cos 2 x = tan x + 1.
Thus,
2 cos 6 x 2 cos 4 x + cos 2 x = ( tan x + 1 ) 3 4 ( tan x + 1 ) 2 2 + tan x + 1 2 =
= tan 3 x + tan 2 x + tan x + 1 4 = 1 2 .

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rmd1228887e
Answered 2022-07-05 Author has 2 answers
From the given condition:
tan x = 1 tan 2 x 1 + tan 2 x = cos 2 x .
Thus:
2 cos 6 x 2 cos 4 x + cos 2 x = cos 2 x ( 2 cos 2 x ( cos 2 x 1 ) + 1 ) =
cos 2 x ( 1 2 sin 2 2 x + 1 ) = 1 2 cos 2 x ( cos 2 2 x + 1 ) = s u b s t i t u t e
1 2 cos 2 x ( tan 2 x + 1 ) = 1 2 .

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