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Joshua Foley 2022-07-10 Answered
determine the roots of the equation 7 sec 2 x + 2 tan x 6 = 2 sec 2 x + 2 when 0 x 2 π
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Ordettyreomqu
Answered 2022-07-11 Author has 22 answers
Using 1 + t a n 2 = s e c 2 ,
7 sec 2 ( x ) + 2 tan ( x ) 6 = 2 sec 2 ( x ) + 2
7 + 7 tan 2 ( x ) + 2 tan ( x ) 6 = 2 + 2 tan 2 ( x ) + 2
5 tan 2 ( x ) + 2 tan ( x ) 3 = 0
( tan ( x ) + 1 ) ( 5 tan ( x ) 3 ) = 0
tan ( x ) = 1  or  tan ( x ) = 3 / 5.
Thus, in [ 0 , 2 π ), x = 3 π / 4 or x = 7 π / 4 or x = tan 1 ( 3 / 5 ) or x = tan 1 ( 3 / 5 ) + π .
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