find all soultions of the equation sec^s x-1=0 in the interval{0,2pi}
To find all the solutions of the equation sec^2x - 1 = 0 in the interval [0, 2π], you can follow these steps:
Step 1: Rewrite the equation as sec^2x = 1.
Step 2: Take the square root of both sides. Remember to consider both the positive and negative square roots.
sqrt(sec^2x) = ±sqrt(1)
This simplifies to:
sec x = ±1
Step 3: Recall the definition of secant. sec x is equal to 1 divided by the cosine of x.
So, the equation can be further rewritten as:
1/cos x = ±1
Step 4: Solve for cos x.
When 1/cos x = 1, cos x = 1.
When 1/cos x = -1, cos x = -1.
Step 5: Identify the values of x for which cos x is equal to 1 and -1.
Cosine is equal to 1 at x = 0 and x = 2π.
Cosine is equal to -1 at x = π.
So, the solutions for the equation in the interval [0, 2π] are x = 0, x = π, and x = 2π.