Final answer:
To find the value of √(1+sin A)/(1-sin A), use the given equation sec A = (m^2+n^2)/(2mn) and solve for sin A. Substitute sin A into the expression and simplify if needed.
Step-by-step explanation:
To find the value of √(1+sin A)/(1-sin A), we need to use the given equation sec A = (m^2+n^2)/(2mn). From this equation, we can solve for sin A and substitute it into the expression. Here are the steps:
- Start with the equation sec A = (m^2+n^2)/(2mn).
- Take the reciprocal of both sides to get cos A = (2mn)/(m^2+n^2).
- Use the Pythagorean trigonometric identity sin^2 A + cos^2 A = 1 to solve for sin A. Substitute cos A from the previous step and solve for sin A.
- Substitute sin A into the expression √(1+sin A)/(1-sin A).
- Simplify the expression further if needed.