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(cot A - tan A)cos A = cosecA-2sinA
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(cot A - tan A)cos A = cosecA-2sinA

User HTeuMeuLeu
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1 Answer

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Prove the given

  • (cot A - tan A)cos A = cosec A - 2sinA

Use identities

  1. sin²A + cos²A = 1
  2. cotA = cosA/sinA
  3. tanA = cosA/sinA
  4. cosecA = 1/sinA

Solution

Simplify the LHS by using the identities above to get the RHS:

  • (cot A - tan A)cosA =
  • (cosA/sinA - cosA/sinA)cosA = Identities 2 and 3
  • (cosA/sinA)cosA - (cosA/sinA)cosA = Distribute
  • cos²A/sinA - sinA = Simplify/cancel
  • (1 - sin²A)/sinA - sinA = Identity 1
  • 1/sinA - sin²A/sinA - sinA = Distribute
  • 1/sinA - sinA - sinA = Simplify/cancel
  • 1/sinA - 2sinA =
  • cosecA - 2sinA Identity 4

Proved

User Piper
by
4.4k points
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