Prove that- cotA-cosA - cotA-cosA - cosecA-1 - cosecA-1

LHS =cotA cosAcotA+cosA =cosAsinA cosAcosAsinA+cosA =cosA(1sinA 1)cosA(1sinA+1) =1sinA 11sinA+1 =cosecA 1cosecA+1=RHS ...

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Circular Measurement of Angle

Prove that: ...

Question

Prove that:
$\frac{c o t A - c o s A}{c o t A + c o s A} = \frac{c o s e c A - 1}{c o s e c A + 1}$

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\frac{c o t A + c o s e c A - 1}{c o t A - c o s e c A + 1} = \frac{1 + c o s A}{s i n A}

\frac{c o t A + c o s e c A - 1}{c o t A - c o s e c A + 1} = \frac{1 + c o s A}{s i n A} = c o s e c θ + c o t θ = \frac{s i n A}{1 - c o s A}

\frac{c o s A - s i n A + 1}{c o s A + s i n A - 1} = c o s e c A + c o t A

\frac{s i n A}{1 - c o s A} = c o s e c A + c o t A

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