How to prove Cot(A+B) =(cotAcotB-1)÷(cotA+cotB)?

1 Answer
Jim G.
Dec 24, 2017

#"see explanation"#

Explanation:

#"consider left hand side"#

#cot(A+B)#

#=(cos(A+B))/(sin(A+B))#

#=(cosAcosB-sinAsinB)/(sinAcosB+cosAsinB)#

#"divide terms on numerator/denominator by "sinAsinB#

#=((cosAcosB)/(sinAsinB)-(sinAsinB)/(sinAsinB))/((sinAcosB)/(sinAsinB)+(cosAsinB)/(sinAsinB))#

#=(cotAcotB-1)/(cotB+cotA)#

#="right hand side "rArr"proven"#

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