Verify the identity? cot(x) sec(x) / csc(x) = 1

1 Answer
Feb 20, 2018

See explanation

Explanation:

We want to verify

cot(x)sec(x)/csc(x)=1

Use the definitions of cotangent, secant and cosecant

  • cot(x)=cos(x)/sin(x)
  • sec(x)=1/cos(x)
  • csc(x)=1/sin(x)

Using these

LHS=cot(x)sec(x)/csc(x)

=cos(x)/sin(x)(1/cos(x))/(1/sin(x))

=(cos(x)1/cos(x))/(sin(x)1/sin(x))

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

=1/1

=1=RHS