Which of the following is a simpler form of the expression sin (theta)sec(theta)÷ cos(theta)tan(theta)

Question

asked Jul 28, 2018 200k views

2 Answers

Nickgroenke · Answer 1 · 2018-07-29T07:35:34+0000

Answer:

The simplified form of the given expression
$(\sin\theta \cdot \sec\theta)/(\cos\theta\cdot \tan\theta)$ is
$\sec\theta$

Explanation:

Given: Expression
$(\sin\theta \cdot \sec\theta)/(\cos\theta\cdot \tan\theta)$

We have to writ the given expression in simplified form.

Consider , The given expression
$(\sin\theta \cdot \sec\theta)/(\cos\theta\cdot \tan\theta)$

Since, we know,

$\sec\theta=(1)/(\cos\theta)$

and
$\tan\theta=(\sin\theta)/(\cos\theta)$

Substitute, we have,

$(\sin\theta \cdot \sec\theta)/(\cos\theta\cdot \tan\theta)=\frac{\sin\theta \cdot(1)/(\cos\theta)} {\cos\theta\cdot (\sin\theta)/(\cos\theta) }$

Simplify, we have,

$=\frac{(1)/(\cos\theta)} {\cos\theta\cdot (1)/(\cos\theta) }$

Simplify further, we get,

$=(1)/(\cos\theta)=\sec\theta$

Thus, The simplified form of the given expression
$(\sin\theta \cdot \sec\theta)/(\cos\theta\cdot \tan\theta)$ is
$\sec\theta$

Zeagord · Answer 2 · 2018-08-02T08:34:40+0000

Answer:
$sec \theta$ .

Explanation: Given expression :
$(sin \theta \ sec \theta )/(cos \theta \ tan \theta) .$

We know,

$sec \theta = (1)/(cos \theta)$

$tan \theta = (sin \theta)/(cos \theta)$

Substituting those values in given expression, we get

$(sin \theta \ sec \theta )/(cos \theta \ tan \theta) .$ =
$\frac{sin \theta\ (1)/(cos \theta) } {cos \theta\ (sin \theta)/(cos \theta) }$

=
$(sin \theta \ cos \theta)/(cos \theta \ cos \theta \ sin \theta)$

Crossing out
$sin \theta \ cos \theta$ from top and bottom, we get

=
$(1)/(cos \theta )$

=
$sec \theta$ .