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