How do you prove the identities?

1) 1- cos²θ ≡ sin²θ
2) (1-sin²θ) tanθ≡ cosθ sinθ

The head librarian at the library of congress has asked her assistant for an interval estimate of the mean number of books checked out each day. the assistant provides the following interval estimate: from 740 to 920 books per day. what is an efficient, unbiased point estimate of the number of books checked out each day at the library of congress?

Aheated piece of metal cools according to the function c(x) = (.5)x ? 7, where x is measured in hours. a device is added that aids in cooling according to the function h(x) = ? x ? 2. what will be the temperature of the metal after two hours?

The cost for an uberi is $2.50 plus $2.00 mile. if the total for the uber ride was $32.50, how many miles did the customer travel?