How do you verify $cscx-sinx=cosxcotx$ ?

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Answer 1 · 2016-04-16T18:22:08

Let's start by stating the identities that will be important to this problem:

The reciprocal identity (1): $cscx = 1/sinx$

The quotient identity (1): $cotx = cosx/sinx$

$1/sinx - sinx = cosx(cosx/sinx)$

Placing the left side on a common denominator:

$1/sinx - sin^2x/sinx = cos^2x/sinx$

$(1 - sin^2x)/sinx = cos^2x/sinx$

Applying the Pythagorean identity $cos^2x + sin^2x = 1$ , we get:

$cos^2x/sinx = cos^2x /sinx$

Hopefully this helps!

How do you verify cscx-sinx=cosxcotxcscx-sinx=cosxcotx?