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

Problem

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

Solution

1. Rewrite the trigonometric functions on the left side in terms of sine and cosine using the fundamental identities.

csc(x)=1/sin(x)

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

2. Substitute these expressions back into the original equation to multiply them.

1/sin(x)⋅sin(x)/cos(x)

3. Simplify the expression by canceling the common factor of sin(x) from the numerator and the denominator.

1/cos(x)

4. Apply the reciprocal identity to express the result as the secant function.

1/cos(x)=sec(x)

Final Answer

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

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