Question

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

Answer 1

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`