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
