Pdawgg
Pdawgg Pdawgg
  • 19-08-2020
  • Mathematics
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Verify the identity. cot x / 1 + csc x = csc x - 1 / cot x

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MathPhys
MathPhys MathPhys
  • 19-08-2020

Step-by-step explanation:

cot x / (1 + csc x)

Multiply by conjugate:

cot x / (1 + csc x) × (1 − csc x) / (1 − csc x)

Distribute the denominator:

cot x (1 − csc x) / (1 − csc²x)

Use Pythagorean identity:

cot x (1 − csc x) / (-cot²x)

Divide:

(csc x − 1) / cot x

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