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Crazy boy [7]
3 years ago
13

7 cos x+1=6 secx solve for x

History
1 answer:
musickatia [10]3 years ago
4 0
Sec x=1/cos x
Then:
7 cos x + 1=6 sec x
7 cos x  + 1=6(1/cosx)
least common multiple=cos x
7 cos² x+cosx=6
7 cos² x + cosx -6=0

cos x=z

7z²+z-6=0
we solve this square equation:

z=[-1⁺₋√(1+168)]/14
z=(-1⁺₋13)/14
we have two solutions:
z₁=(-1-13)/14=-1

cos x=-1
x=arc cos (-1)=180º =π
Solution1=180º+2Kπ    K∈Z

z₂=(-1+13)/14=12/14
cos x=12/14
x=arc cos (12/14)=31º
Solution2=31º+2kπ

Answer: solution1Usolution2= 31º+2Kπ U 180º+2Kπ;    K∈Z

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