Respuesta :
The simpler form of the expression [tex]\rm \frac{sin\theta sec\theta}{cos\theta tan\theta}[/tex] is [tex]\\\rm sec\theta[/tex].
It is given that the expression [tex]\rm \frac{sin\theta sec\theta}{cos\theta tan\theta}[/tex]
It is required to find the simpler form from the given options.
What is the trigonometric ratio?
The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
We have the expression:
[tex]\rm= \frac{sin\theta sec\theta}{cos\theta tan\theta}[/tex]
We know:
[tex]\rm cos\theta = \frac{1}{sec\theta} \\\\\rm tan\theta = \frac{sin\theta}{cos\theta}[/tex]
By using these trigonometry formulas, we get:
[tex]\rm= \frac{sin\theta sec\theta}{cos\theta tan\theta}\\\\\rm= \frac{sin\theta }{(cos\theta) (cos\theta) \frac{sin\theta }{cos\theta} }\\\\\rm= \frac{1}{cos\theta} \\\\\rm = sec\theta[/tex]
Thus, the simpler form of the expression [tex]\rm \frac{sin\theta sec\theta}{cos\theta tan\theta}[/tex] is [tex]\\\rm sec\theta[/tex].
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