Verify the Identity? Sinx / 1-cos^2x = cscx

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Verify the Identity? Sinx / 1-cos^2x = cscx

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Answer 1 · 2018-02-23T00:27:07

To solve this, we need to use the Pythagorean Trig Identity.

Explanation:

The Pythagorean Identity states:

$cos^2x + sin^2x = 1$

We manipulate this to get either $cos^2x$ or $sin^2x$ by itself. For this problem, we want $sin^2x$ by itself. To do this, we can simply subtract the $cos^2x$ over to the other side, making it:

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

Knowing this, we can verify the trigonometric equation. Since we now know that $1-cos^2x$ equals $sin^2x$ , we can substitute that in, giving us:

$sinx / sin^2x = cscx$

From here, we can do a simple cancellation of a $sinx$ in the numerator and denominator, which leaves us with:

$1 / sinx = cscx$

And then:

$cscx = cscx$

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Verify the Identity? Sinx / 1-cos^2x = cscx

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