Solve (secx)^2 tanx = 3

Evaluate

sec^{2} (x) tan (x) = 3

Find the domain

sec^{2} (x) tan (x) = 3, x \neq = \frac{π}{2} + kπ, k \in Z

Use sec^{2} (x) = tan^{2} (x) + 1 to rewrite the expression

tan^{3} (x) + tan (x) = 3

Move the expression to the left side

tan^{3} (x) + tan (x) - 3 = 0

Calculate

tan (x) \approx 1.213412

Use the inverse trigonometric function

x = arctan (1.213412)

Add the period of kπ, k \in Z to find all solutions

x = arctan (1.213412) + kπ, k \in Z

Check if the solution is in the defined range

x = arctan (1.213412) + kπ, k \in Z, x \neq = \frac{π}{2} + kπ, k \in Z

Solution

x = arctan (1.213412) + kπ, k \in Z

Alternative Form

x \approx 0.881519 + kπ, k \in Z

Alternative Form

x \approx 50.50729 3^{\circ} + 18 0^{\circ} k, k \in Z

Solve the equation