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Solve on the interval 0 2pi. 2sec(x)+6=2

User Zetar
by
6.6k points

1 Answer

7 votes

Answer:

x =
(2\pi )/(3), x =
(4\pi )/(3)

Explanation:

using the trigonometric identity

• sec x =
(1)/(cosx)

isolate sec x by subtracting 6 from both sides and dividing both sides by 2

2sec x = - 4 ⇒ sec x = - 2, hence


(1)/(cosx) = - 2

⇔ cosx = -
(1)/(2)

since cos x < 0 then x is in second/ third quadrant

x =
(2\pi )/(3) or x =
(4\pi )/(3)



User Aaron Adams
by
7.4k points