Make the indicated trigonometric substitution in squareroot

Make the indicated trigonometric substitution in squareroot x^2 - 25/x, x = 5 sec(theta) Use an Addition or Subtraction Formula to find the cos(285 degree)

Solution

x = 5sec(theta)

sqrt[( x^2 - 25)]/x

Substitute x in above formula:

sqrt[( 25sec^2(theta) - 25)]/5sectheta

= 5 sqrt(sec^2theta -1)/5sectheta

we know that : 1 +tan^2theta = sec^2theta

So, sqrt(sec^2theta -1)/sectheta

sqrt(tan^2(theta)/sectheta

= tan(theta)/sectheta

= sin(theta)