Question 769371
prove that (cos A cot A)/(1-sin A) = 1 + cosec A
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{{{cos(A)cot(A)/(1-sin(A))=1+csc(A)}}}
start with left hand side
{{{cos(A)cot(A)/(1-sin(A))}}}
{{{(cos(A)cos(A)/sin(A))/(1-sin(A))}}}
{{{(cos^2(A)/sin(A))/(1-sin(A))=(1-sin^2(A))/(sin(A))/(1-sin(A))
=(1-sin^2(A))(1+sin(A))/(sin(A))/(1-sin(A))(1+sin(A))
=(1-sin^2(A))(1+sin(A))/(sin(A))/(1-sin^2(A))
=(1+sin(A))/(sin(A))=(1/sin(A))+1}}}
=1+csc(A)
Verified: left hand side=right hand side