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Landon Bonilla

Landon Bonilla

Answered question

2022-05-21

( cos 2 x + cos x 1 ) / ( cos 2 x ) > 2 for x < 0 , π >

Answer & Explanation

exhumatql

exhumatql

Beginner2022-05-22Added 12 answers

HINT:
cos ( 2 x ) + cos ( x ) 1 cos ( 2 x ) > 2
( cos ( 2 x ) + cos ( x ) 1 ) sec ( 2 x ) > 2
( cos ( x ) 1 ) sec ( 2 x ) + 1 > 2
( cos ( x ) 1 ) sec ( 2 x ) > 1
So know we can find the four possible solutions for the 'overall' problem:
2 π n 3 π 4 < x < 1 2 ( 4 π n π )
2 π n + π 4 < x < 1 3 ( 6 π n + π )
1 3 ( 6 π n π ) < x < 2 π n π 4
1 2 ( 4 π n + π ) < x < 2 π n + 3 π 4
With n Z

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