To solve an equation in a given interval, you will need to use the properties of the trigonometric functions and apply them to the given equation. In this case, you will need to use the double angle formula for secant and the identity for tangent.
The first step in solving this equation is to rewrite it in terms of one variable, preferably either secant or tangent. In this case, we can rewrite the equation as sec²A - 3tanA - 5 = 0.
The double angle formula for secant is sec²2x = 1 + tan²x. In this equation, we can replace sec²A with 1 + tan²A to simplify the equation.
Yes, you can use a calculator to solve this equation. However, you will need to use the inverse trigonometric functions to solve for the angle A. You can use the inverse secant and inverse tangent functions on your calculator to find the values of A.
Yes, since we are solving in the interval [-90,0], the values of A must fall within this range. Additionally, the tangent function is undefined at ±90 degrees, so we must exclude these values from our solutions.