Question

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

Answer 1

Answer: $sec \theta$.

Step-by-step explanation: Given expression : $\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .$

We know,

$sec \theta = \frac{1}{cos \theta}$

$tan \theta = \frac{sin \theta}{cos \theta}$

Substituting those values in given expression, we get

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

= $\frac{sin \theta \ cos \theta}{cos \theta \ cos \theta \ sin \theta}$

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

=$\frac{1}{cos \theta }$

= $sec \theta$.

Answer 2

Answer:

The simplified form of the given expression $\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}$ is  $\sec\theta$

Step-by-step explanation:

Given: Expression $\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}$

We have to writ the given expression in simplified form.

Consider , The given expression $\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}$

Since, we know,

$\sec\theta=\frac{1}{\cos\theta}$

and  $\tan\theta=\frac{\sin\theta}{\cos\theta}$

Substitute, we have,

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

Simplify, we have,

$=\frac{\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{1}{\cos\theta} }$

Simplify further, we get,

$=\frac{1}{\cos\theta}=\sec\theta$

Thus, The simplified form of the given expression $\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}$ is  $\sec\theta$