prove that cot A minus Cos A upon cot A + Cos A = cosecA-1/cosecA+1
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____Here's your Answer ________
L.H.S.
(Cot A - CosA) / (cot A + cos A)
=> (CosA/SinA - CosA) / (CosA/sinA + cosA)
=>[ (CosA - CosA×SinA)/SinA] / [ ( cosA + cosA × sinA)/sinA]
=> (CosA - CosA × SinA ) / ( cosA + cosA × SinA)
=> CosA( 1 - SinA) / CosA( 1 + sinA)
=> 1 - sinA / 1 + SinA
Dividing Denominator and Numerator by SinA
=> [(1 - sinA)/ sinA] / [( 1 + sinA)/sinA ]
=> (1/sinA - SinA/sinA) / ( 1/sinA + sinA/sinA)
=> ( 1/sinA - 1 ) / ( 1/sinA + 1)
=> (cosecA - 1) / (cosecA + 1)
✔✔✔
____Here's your Answer ________
L.H.S.
(Cot A - CosA) / (cot A + cos A)
=> (CosA/SinA - CosA) / (CosA/sinA + cosA)
=>[ (CosA - CosA×SinA)/SinA] / [ ( cosA + cosA × sinA)/sinA]
=> (CosA - CosA × SinA ) / ( cosA + cosA × SinA)
=> CosA( 1 - SinA) / CosA( 1 + sinA)
=> 1 - sinA / 1 + SinA
Dividing Denominator and Numerator by SinA
=> [(1 - sinA)/ sinA] / [( 1 + sinA)/sinA ]
=> (1/sinA - SinA/sinA) / ( 1/sinA + sinA/sinA)
=> ( 1/sinA - 1 ) / ( 1/sinA + 1)
=> (cosecA - 1) / (cosecA + 1)
✔✔✔
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