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#