Question

Use trigonometric expressions to build an equivalent trigonometric identity with the given expression: sec (x) tan (x) cos (x) csc (x) =

Answer 1

Explanation:

Step 1: Simplify all of the trigonometric functions

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

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

`cos(x) = cos(x)`

`csc(x) = (1)/(sin(x))`

`(1)/(cos(x))*(sin(x))/(cos(x))*(cos(x))/(1)*(1)/(sin(x))`

`(sin(x)cos(x))/(cos(x)cos(x)sin(x))`

`(1)/(cos(x))`

`sec(x)`

Answer:
`sec(x)`

Answer 2

sec (x)

Explanation:

sec (x) tan (x) cos (x) csc (x) =

We know sec = 1/ cos

Tan = sin/cos

csc = 1/sin

Replacing into the expression

1/ cos (x) * sin(x)/ cos (x) * cos (x) * 1 / sin(x)

Canceling like terms

1/ cos (x)

sec(x)