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Which results from multiplying the six trigonometric functions

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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.

User Adeel Siddiqui
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