Verify the Identity tan(x)cos(x)csc(x)=1

Problem

tan(x)*cos(x)*csc(x)=1

Solution

1. Rewrite the tangent function in terms of sine and cosine using the quotient identity tan(x)=sin(x)/cos(x)

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

2. Simplify the expression by canceling the cos(x) terms in the numerator and denominator.

sin(x)/cos(x)⋅cos(x)⋅csc(x)=sin(x)⋅csc(x)

3. Rewrite the cosecant function using the reciprocal identity csc(x)=1/sin(x)

sin(x)⋅csc(x)=sin(x)⋅1/sin(x)

4. Simplify the product by canceling the sin(x) terms to reach the final value.

sin(x)⋅1/sin(x)=1

Final Answer

tan(x)*cos(x)*csc(x)=1

Want more problems? Check here!