What is the missing justification in the proof of the pythagorean identity below, sin^2x+cos^2x=1, using a right triangle?

  a)  substitution property of equality

Step-by-step explanation:

It looks like an expression has been formed using the left sides of the first two statements, and then the right sides of those statements substituted into that expression. Hence, it seems the substitution property is the most appropriate choice.

 

You have to jusitfy the step that leads from sin (x) = a/c and cos(x) = b/c to sin^2 (x) + cos^2(x) = [a^2 / c^2] + [b^2 / c^2].

As you can see go from the first statement to the second by substituting the value of sin(x) by a/x and the value of cos(x) by b/c.

Then, the answer is the option b. substitution property of equality.