Sin A/1-cos A = cosec A + cot A
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Explanation:
We want to verify the identity
#sin(a)/(1+cos(a))=csc(a)-cot(a)#
We will use
#sin^2(a)+cos^2(a)=1#
And the basic definitions of trigonometric functions
#LHS=sin(a)/(1+cos(a))#
#=(sin(a)(1-cos(a)))/((1+cos(a))(1-cos(a)))#
#=(sin(a)-sin(a)cos(a))/(1-cos^2(a))#
#=(sin(a)-sin(a)cos(a))/sin^2(a)#
#=sin(a)/sin^2(a)-(sin(a)cos(a))/sin^2(a)#
#=1/sin(a)-cos(a)/sin(a)#
#=csc(a)-cot(a)=RHS#
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