Question

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

Answer 1

Answer:

sec (x)

Step-by-step 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)

Answer 2

Step-by-step explanation:

Step 1:  Simplify all of the trigonometric functions

$sec(x) = \frac{1}{cos(x)}$

$tan(x) = \frac{sin(x)}{cos(x)}$

$cos(x) = cos(x)$

$csc(x) = \frac{1}{sin(x)}$

$\frac{1}{cos(x)}*\frac{sin(x)}{cos(x)}*\frac{cos(x)}{1}*\frac{1}{sin(x)}$

$\frac{sin(x)cos(x)}{cos(x)cos(x)sin(x)}$

$\frac{1}{cos(x)}$

$sec(x)$

Answer:  $sec(x)$