Question

Verify the following identity. Show all work for credit.

sin cot sec = 1

Answer 1

Prove
`sin(x)cot(x)sec(x)=1`

Using the following trig identities:

`cot(x)=(1)/(tan(x))`

`sec(x)=(1)/(cos(x))`

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

`\implies sin(x)cot(x)sec(x)=sin(x) \cdot (1)/(tan(x)) \cdot(1)/(cos(x))`

`= (1)/(tan(x)) \cdot(sin(x))/(cos(x))`

`= (1)/(tan(x)) \cdot tan(x)`

`= (tan(x))/(tan(x))`

`=1`

Hence
`sin(x)cot(x)sec(x)=1`

Answer 2

Formula's:

• 
  `\rm cot = (cos)/(sin)`

• 
  `\rm sec = (1)/(cos)`

solve:

`\rightarrow \rm sin \ cot \ sec = 1`

`\rightarrow \rm sin \ (cos)/(sin) \ (1)/(cos) = 1`

`\rightarrow \rm (sin \ cos)/(sin \ cos) = 1`

`1 = 1`

L.H.S = R.H.S

Hence both sides are equal and confirmed true. identify proved.