Question 1150576
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{{{cos(A+B)/cos(A)sin(B)=cot(B) - tan(A)}}}

Work with the left side

Use formula for cos(A+B)

{{{(cos(A)cos(B)-sin(A)sin(B))/(cos(A)sin(B))}}}

Break into two fractions:

{{{(cos(A)cos(B))/(cos(A)sin(B))-(sin(A)sin(B))/(cos(A)sin(B))}}}

Cancel cos(A)'s in the first fraction and sin(B)'s in second fraction:

{{{(cross(cos(A))cos(B))/(cross(cos(A))sin(B))-(sin(A)cross(sin(B)))/(cos(A)cross(sin(B)))}}}

{{{(cos(B))/(sin(B))-(sin(A))/(cos(A))}}}

Use quotient identities for cotangent and tangent:

{{{cot(B) - tan(A)}}}

Edwin</pre>