Question

What is the solution of 2sin square(x)-cosx-1=0
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Answer 1

`{ \rm{2 { \sin }^(2) x - \cos x - 1 = 0 }} \\ \\ { \rm{2(1 - { \cos }^(2) x) - \cos x - 1 = 0}} \\ \\ { \rm{2 - 2 { \cos}^(2) x - \cos x - 1 = 0}} \\ \\ { \rm{2 { \cos }^(2)x + \cos x - 1 = 0 }} \\`

• solving using quadratic formula:

`{ \boxed{ \rm{x = \frac{ - b \pm \sqrt{ {b}^(2) - 4ac} }{2a} }}} \\ \\ { \rm{ \cos(x) = (1 \pm √(9) )/(8) }} \\ \\ { \rm{ \cos(x) = (1)/(2) \: \: or \: \: (1)/(4) }} \\ \\ { \boxed{ \tt{x = 60 \degree \: and \: \: 75.5 \degree}}}`