Solve the equation on the interval [ 0 , 2 π ) tan ⁡ x...

Ashlyn Krause

Ashlyn Krause

Answered

2022-07-27

Solve the equation on the interval [ 0 , 2 π )
tan x + sec x = 1

Answer & Explanation

Minbutastc

Minbutastc

Expert

2022-07-28Added 14 answers

Given equation is tan x + sec x = 1
sin x cos x + 1 cos x = 1
sin x + 1 = cos x
sin x cos x = 1
squaring on both sides, we get
( sin x cos x ) 2 = ( 1 ) 2
sin 2 x + cos 2 x 2 sin x cos x = 1
1 2 sin x cos x = 1
2 sin x cos x = 0
sin 2 x = 0
2 x = sin 1 ( 0 )
2 x = 0 , π , 2 π
x = 0 , π 2 , π

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