rhysejhugroo
rhysejhugroo
10-07-2022
Mathematics
contestada
(cot A - tan A)cos A = cosecA-2sinA
Respuesta :
mhanifa
mhanifa
10-07-2022
Prove the given
(cot A - tan A)cos A = cosec A - 2sinA
Use identities
sin²A + cos²A = 1
cotA = cosA/sinA
tanA = cosA/sinA
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
Answer Link
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