Pre- Calculus Help Please!?

[be H]

Verify that each x-value ia a solution of the equation

2cosx-1=0

3tan(^2)2x-1=0

sec^4x-3sec^2x-4=0

 

[Michael Reid]

You need to provide the x values so we can see if they satisfy the equation.

 

[mohanrao d]

a)

2cos x - 1 = 0

2cos x = 1

cos x = 1/2

x = Î*/3, 5Î*/3 in the interval [0, 2Î* ]


b)

3tan^2(2x) - 1 = 0

3tan^2(2x) = 1

tan^2(2x) = 1/3

tan (2x) = 1/√3, -1/√3

2x = Î*/6, 5Î*/6, 7Î*/6, 11Î*/6, 13Î*/6, 17Î*/6, 19Î*/6, 23Î*/6

x = Î*/12, 5Î*/12, 7Î*/12, 11Î*/12, 13Î*/12, 17Î*/12, 19Î*/12, 23Î*/12 in the interval [0, 2Î* ]

c)

sec^4(x) - 3sec^2(x) - 4 = 0

( sec^2(x) + 1)(sec^2(x) - 4) = 0

sec^2(x) = 4 is only valid solution

sec x = 2 or -2

cos x = 1/2 or -1/2

x = Î*/3, 2Î*/3, 4Î*/3 and 5Î*/3 in the interval [0, 2Î* ]