Math, asked by Abhimanyu43, 1 year ago

prove that cot A minus Cos A upon cot A + Cos A = cosecA-1/cosecA+1

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Answered by gautamkumar0219
1
proved attached above
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Answered by UltimateMasTerMind
8
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(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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