Pre-cal

posted by .

find all solutions of equation in [0, 2pi)
2 (sec x)^2 + (tan x)^2 -3 = 0

• Pre-cal -

since sec^2 x = 1+tan^2 x, we have

2(1+tan^2 x)+tan^2 x-3=0
3tan^2 x-1 = 0
tan^2 x = 1/3
tan x = ±1/√3

tan x > 0 in QI, QIII, so
x = π/6, 7π/6

tan x < 0 in QII, QIV, so
x = 5π/6, 11π/6

Actually, since the period of tan x is
π, it would be better to ask for solutions in [0,π) rather than 2π.

Similar Questions

1. Integration

Intergrate ¡ì sec^3(x) dx could anybody please check this answer. are the steps correct?
2. Pre-Cal

Perform the addition or subtraction. tanx - sec^2x/tanx tan^2(x)/tan(x) - sec^2x/tanx = tan^2x sec^2x / tanx then I use the identity 1+tan^2u=sec^2u I do not know what to do at this point.
3. Pre-cal/Trig

(tan/(1+sec)) + ((1+sec)/tan) = 2csc (Show all work please.)
4. pre cal 2

Find all solutions in the interval [0, pi], 2sec^2x+tan^2x-3=0
5. pre cal 2

Find all solutions in the interval [0, pi], 2sec^2x+tan^2x-3=0
6. pre cal 2

Find all solutions in the interval [0, pi], 2sec^2x+tan^2x-3=0
7. pre cal

Find all solutions in the interval[0,2pi),cos x/2-sinx=0
8. pre cal 2

Find all solutions in the unterval [0,2pi), cos x/2-sinx=0
9. Math (Pre-Calc)

Find all the solutions of the equation in the interval {o,2pi) 5sqrt3 tan x+3=8sqrt3 tan x
10. math

Find all solutions to the equation tan(t)=1/tan (t) in the interval 0<t<2pi. Solve the equation in the interval [0, 2pi]. The answer must be a multiple of pi 2sin(t)cos(t) + sin(t) -2cos(t)-1=0 Find all solutions of the equation …

More Similar Questions