what would be the first step in verifying the following identity? cos(x)*tan(x)=sin(x) Multiplication Substitution Evaluation  This is not an identiy

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You may select two options when solving the problem: either multiplication, or substitution, both options work perfectly.

Selecting the multiplication option, you will need to multiply both sides by 1/cos x such that:

(cos x*tan x)/cos x = sin x/cos x

Reducing like terms yields:

tan x = sin x/cos x

This last line represents the definition of tangent function, hence the given expression is an identity.

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on


You could also use substitution: 

tan(x) = sin(x)/cos(x)

cos(x) * sin(x)/cos(x) = sin(x)

The cosx cancels and you are left with 

sin(x) = sin(x) 

Since this is a true statement, we've probed that the premise is true. 

emanuel-'s profile pic

emanuel- | Student, College Freshman | (Level 2) eNoter

Posted on


tan(x) = sin(x)/cos(x)

replace in the original equation:


cos(x) simplifies with the denominator =>sin(x)=sin(x)

The answer is Substitution

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