Master The Pythagorean Identity With This Trig Identity Formula: Csc^2X = (1-Sin^2X)/Sin^2X

csc^2x

1+cot^2x

Recall the Pythagorean Identity:

– sin^2x + cos^2x = 1

Dividing both sides by cos^2x, we get:

– sin^2x/cos^2x + cos^2x/cos^2x = 1/cos^2x

Using trig identities:

– tan^2x + 1 = sec^2x

Substituting in sin^2x/cos^2x for tan^2x:

– sin^2x/cos^2x + 1 = sec^2x

Subtracting 1 from both sides:

– sin^2x/cos^2x = sec^2x – 1

Now we can substitute in the reciprocal identity for secant:

– sin^2x/cos^2x = (1/cos^2x) – 1

Combining like terms:

– sin^2x/cos^2x = (1-cos^2x)/cos^2x

Using the Pythagorean Identity again:

– sin^2x/cos^2x = sin^2x/(1-sin^2x)

Therefore:

– csc^2x = (1-sin^2x)/sin^2x

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