Question 667144
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Hi, there--

The Problem

Simplify this expression.
{{{sin(A)+tan(A)cos(A)+(sin(A)cos(A)sec(A))/(sin(A)tan(A))}}}

There is some ambiguity about what parts of the expression you mean to by the "over." 
This is the expression that I simplified. If this is not your expresso, feel free to email me back 
and I'll resolve.

Solution:
Substitute sin(A)/cos(A) for tan (A).
{{{sin(A)+(sin(A)/cos(A))cos(A)+(sin(A)cos(A)sec(A))/(sin(A)(sin(A)/cos(A)))}}}

Cancel like terms in the numerator and denominator.
{{{sin(A)+sin(A)+(sin(A)cos(A)sec(A))/(sin(A)(sin(A)/cos(A)))}}}

Simplify the double division in the third term.
{{{sin(A)+sin(A)+(sin(A)cos^2(A)sec(A))/(sin^2(A))}}}

Substitute 1/cos(A) for sec(A).
{{{sin(A)+sin(A)+(sin(A)cos^2(A))/(sin^2(A)cos(A))}}}

Combine like terms.
{{{2sin(A)+(sin(A)cos^2(A))/(sin^2(A)cos(A))}}}

Cancel like terms in the numerator and denominator.
{{{2sin(A)+cos(A)/sin(A)}}}

Substitute cot(A) for cos(A)/sin(A)
{{{2sin(A)+cot(A)}}}

All the Best,
Mrs.Figgy
math.in.the.vortex@gmail.com
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