Verify the Identity (tan(A))/(sec(A))=sin(A)

Problem

tan(A)/sec(A)=sin(A)

Solution

1. Express the numerator tan(A) in terms of sine and cosine using the quotient identity.

tan(A)=sin(A)/cos(A)

2. Express the denominator sec(A) in terms of cosine using the reciprocal identity.

sec(A)=1/cos(A)

3. Substitute these identities into the left side of the original equation.

tan(A)/sec(A)=sin(A)/cos(A)/1/cos(A)

4. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

sin(A)/cos(A)⋅cos(A)/1

5. Cancel the common factor cos(A) from the numerator and the denominator.

sin(A)

Final Answer

tan(A)/sec(A)=sin(A)

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