Sin A /1+cos A = cosec A - cot A ?

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Answer 1 · 2018-02-22T08:56:29

See explanation

We want to verify the identity

#sin(a)/(1+cos(a))=csc(a)-cot(a)#

We will use

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#