Make the indicated trigonometric substitution in the given algebraic expression and simplify (x-25) / x = Sin y0

x = 25 / (1 - sin (y)) and y ≠ π/2 + 2πn

Step-by-step explanation:

Let's solve and simplify for x,

(x - 25) / x = sin (y)

Let's multiply both sides by x

((x - 25) / x) * x = sin (y) * x

Then,

x - 25 = sin (y) * x

Let's add 25 to both sides

x - 25 + 25 = sin (y) * x + 25

If simplify again,

x = sin (y) * x + 25

Then we need subtract sin y x from both sides

x - sin (y) * x = sin (y) * x + 25 - sin (y) * x

It will equal:

x - sin (y) * x = 25

Factor x-sin (y) x: x (1-sin (y)), then we get:

x (1 - sin (y)) = 25

Finally we need divide both sides by 1 - sin (y); y ≠π / 2 + 2πn

And it will give us this equation:

x = 25 / (1 - sin (y)) and y ≠ π/2 + 2πn