Multiplying the six trigonometric functions (sine, cosine, tangent, cotangent, secant, and cosecant) together would result in a product that is a constant. Specifically, the product is always equal to 1.
To see why, consider the following identities:
sin(x) * csc(x) = 1
cos(x) * sec(x) = 1
tan(x) * cot(x) = 1
We can rewrite these identities as:
sin(x) = 1/csc(x)
cos(x) = 1/sec(x)
tan(x) = 1/cot(x)
Substituting these expressions into the product of the six trigonometric functions, we get:
sin(x) * cos(x) * tan(x) * cot(x) * sec(x) * csc(x)
= (1/csc(x)) * (1/sec(x)) * (1/cot(x)) * (cot(x)) * (1/sec(x)) * (1/csc(x))
= 1
Therefore, the product of the six trigonometric functions is always equal to 1.