Verify the pythagorean identity.

1 + cot^2 0 = csc^2 6

To prove this Pythagorean Identity, we have to know that:

cot = 1 / tan

and we also know that:

tan = sin / cos

Therefore,

cot = 1 / tan = cos / sin

So we can write the given equation in the form of:

1 + (cos^2 θ / sin^2 θ) = csc^2 θ

Expanding the left hand side of the equation:

(sin^2 θ / sin^2 θ) + (cos^2 θ / sin^2 θ) = csc^2 θ

(sin^2 θ + cos^2 θ) / sin^2 θ = csc^2 θ

We know that given a unit circle, sin^2 θ + cos^2 θ = 1. So:

1 / sin^2 θ = csc^2 θ

The equation above is already true basing on the trigonometric identities. Therefore:

csc^2 θ = csc^2 θ

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.