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Solving a Quadratic Equation by Factorization Method

Prove that 1 ...

Question

Prove that 1÷cosec A-cot A -1÷sin A =1÷sin A -1÷cosex A+cot A

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Solution

LHS=1/(cosecA-cotA) -1/sinA =(cosecA+cotA)/cosec^2A-cot^2A) -cosecA
=cosecA+cotA-cosecA
=cotA
RHS=1/sinA-1/(cosecA+cotA)
=cosecA-(cosecA-cotA)/(cosec^2A-cot^2A)
=cosecA-(cosecA-cotA)
=cotA
LHS=RHS

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