find all solutions of the equation
tan(sq)x=1
To find all solutions of the equation tan^2x = 1, we need to first isolate the variable x.
Step 1: Write the equation as a quadratic equation.
tan^2x - 1 = 0
Step 2: Apply the identity tan^2x = sec^2x - 1.
(sec^2x - 1) - 1 = 0
sec^2x - 2 = 0
Step 3: Solve for sec^2x.
sec^2x = 2
Step 4: Take the square root of both sides.
secx = ±√2
Step 5: Take the reciprocal of both sides to get the cosine.
cosx = ±1/√2
Step 6: Simplify the square root.
cosx = ±√2/2
Step 7: Determine the values of x using the unit circle or trigonometric identity values.
The values of x where cosx = √2/2 are π/4 and 7π/4.
The values of x where cosx = -√2/2 are 3π/4 and 5π/4.
Therefore, the solutions to the equation tan^2x = 1 are:
x = π/4 + nπ, where n is an integer
x = 3π/4 + nπ, where n is an integer
x = 5π/4 + nπ, where n is an integer
x = 7π/4 + nπ, where n is an integer