Simplify the expression sine of x to the second power minus one divided by cosine of negative x

First, let us express it into mathematical terms: (sinx) ^2 - 1 : cos (-x)

In trigonometry, there are symmetrical functions. Cosine is one of them. This is when cos (-x) is equal to - cosx. This is only true for cosine functions only and not to other trigonometric functions. Also, in pythagorean theorems, (sinx) ^2 + (cosx) ^2 = 1. Therefore, (sinx) ^2 - 1 = - (cosx) ^2. Therefore, in simplification,

- (cosx) ^2/-cosx = cos x

The simplified answer is then cosine of x. This was solved using the definition of symmetrical functions and the pythagorean theorem.