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Jaidyn Bush

Jaidyn Bush

Answered question

2022-05-24

f ( x ) = tan x sec x , where 0 x 360 . Find values of x, for which f is an increasing function

Answer & Explanation

stacan6t

stacan6t

Beginner2022-05-25Added 13 answers

Let u = sec ( x ). Then, you're trying to solve u ( 2 u 2 1 ) 0, which has solutions
1 2 u 0  or  u 1 2
As either sec ( x ) 1 < 1 2 or sec ( x ) 1 > 1 2 , the above inequality will be satisfied exactly when sec ( x ) is positive:
sec ( x ) = 1 cos ( x ) > 0 cos ( x ) > 0
Therefore, all we have to do is consider where on the unit circle cos ( x ) is positive: 0 x < 90 and 270 < x 360

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