How do you verify $csc^2(theta)(1-cos^2(theta))=1$ ?

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Answer 1 · 2015-11-06T22:57:14

True

$csc^2(theta)*(1-cos^2(theta))=1$

1) Solve on the left side. Notice the Pythagorean Identity.

$1-cos^2(theta) = sin^2(theta)$ , this is just a jumbled version of $sin^2x +cos^2x = 1$ identity.

2) implement the new value so that everything is sine on the left side.

$1/sin^2(theta)*sin^2(theta)/1 -> sin^2(theta)/sin^2(theta) -> 1$

It sounds like you just need to memorize the identities so you can spot them more easily in the future.

How do you verify csc^2(theta)(1-cos^2(theta))=1csc^2(theta)(1-cos^2(theta))=1?