Is the following identity ever undefined? \( 6 \sin ^{2} A+6 \cos ^{2} A-5=1 \) Answer: Select Final check

This identity simplifies using the fundamental Pythagorean identity, \( \sin^2 A + \cos^2 A = 1 \). By substituting this into your equation, we get \( 6(1) - 5 = 1 \), which simplifies to \( 1 = 1 \). Since this holds true for any angle \( A \), the identity is defined for all values of \( A \) and is never undefined. While trigonometric functions like sine and cosine themselves are defined for all real numbers, keep in mind that their inverses (like arcsine and arccosine) are not defined for values outside the range [-1, 1]. Therefore, when dealing with equations involving these inverses, checking the range of outputs is essential! For further insight into how identities work, consider exploring the unit circle, where sine and cosine values correspond to coordinates of points on the circumference. Another fun way to reinforce this concept is by playing trigonometric identities bingo – a classroom game where you solve for identities to cover spaces on your card!