Verify the Identity tan(x)*csc(x)=sec(x)

Problem

tan(x)*csc(x)=sec(x)

Solution

1. Rewrite the left side of the equation using fundamental trigonometric identities.

2. Substitute the identity tan(x)=sin(x)/cos(x) into the expression.

3. Substitute the identity csc(x)=1/sin(x) into the expression.

4. Multiply the two fractions together.

sin(x)/cos(x)⋅1/sin(x)

5. Cancel the common factor of sin(x) from the numerator and the denominator.

1/cos(x)

6. Apply the reciprocal identity 1/cos(x)=sec(x) to complete the verification.

Final Answer

tan(x)*csc(x)=sec(x)

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