Question

Given sine of theta equals 3 over 5 and cosine of theta equals 4 over 5 comma which of the following can be proven using a pythagorean identity? 1 plus the quantity 5 over 13 end quantity squared equals the quantity 12 over 13 end quantity squared 1 plus the quantity 12 over 13 end quantity squared equals the quantity 5 over 13 end quantity squared the quantity 5 over 13 end quantity squared minus the quantity 12 over 13 end quantity squared equals 1 the quantity 5 over 13 end quantity squared plus the quantity 12 over 13 end quantity squared equals 1

Answer 1

The option that can be proven using a Pythagorean identity is 1 plus the quantity 5/13 squared equals the quantity 12/13 squared.

Step-by-step explanation:

To determine which of the given options can be proven using a Pythagorean identity, we need to check if the equation matches the form of the Pythagorean theorem, which states that a² + b² = c². In this case, we are given the sine and cosine of theta, which are defined as the opposite side over the hypotenuse and the adjacent side over the hypotenuse, respectively.

By substituting the given values of sine and cosine into the Pythagorean theorem equation, we can simplify it and see if it matches any of the given options.

Using the given values, we have (3/5)² + (4/5)² = c². This simplifies to (9/25) + (16/25) = c², which becomes 25/25 = c², or 1 = c².

Comparing this to the given options, we see that the equation which matches is 1 plus the quantity 5/13 squared equals the quantity 12/13 squared.