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anonymous
 one year ago
Find all solutions in the interval [0, 2pi).
tan x + sec x = 1
anonymous
 one year ago
Find all solutions in the interval [0, 2pi). tan x + sec x = 1

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0MY WORK: (sin x/ cos x) + (1/ cos x) = 1 (sin x + 1)/ cos x = 1 Then, I'm stuck. :(

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.0subtract sec(x) from both sides first tan(x) = 1  sec(x) then square both sides tan^2(x) = (1secx)^2 = 1  2secx + sec^x then use the trigonometric identity tan^(x) = sec^2(x)1 to change the left side sec^2(x)  1 = 1  2secx + sec^x can you finish from here?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.0ah, a bit of a typo last expression should be sec^2(x)  1 = 1  2secx + sec^2(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So what I was doing is wrong?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.0well, not "wrong" but it would be difficult to get an answer by converting tan(x) and sec(x) into sin(x) and cos(x)

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.0there might be a way to do it your way, but I can't think of an easy way to go from there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait, so will it be equal to 0?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.0sec^2(x)  1 = 1  2secx + sec^2(x) cancel out sec^2(x) 1 = 1  2sec(x) 2sec(x) = 2 sec(x) = 1 then solve for x
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