Which of the following is a simpler form of the expression sin(0)sec(0)/cos(0)tan(0)

[tex]\dfrac{\sin\theta\sec\theta}{\cos\theta\tan\theta}\\\\\text{We know}\ \tan\theta=\dfrac{\sin\theta}{\cos\theta}.\ \text{Substitute:}\\\\=\dfrac{\sin\theta\sec\theta}{\cos\theta\cdot\frac{\sin\theta}{\cos\theta}}=\dfrac{\sin\theta\sec\theta}{\cos\theta}\cdot\dfrac{\cos\theta}{\sin\theta}\\\\\text{Cancel}\ \cos\theta\ \text{and}\ \sin\theta\\\\=\sec\theta[/tex]

ap8997154 ap8997154 · Answer 2 · 2022-07-25T09:33:06+02:00

The trigonometric function gives the ratio of different sides of a right-angle triangle. The correct option is A.

What are Trigonometric functions?

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

The given expression can be simplified as shown below,

[tex]\dfrac{\sin(\theta) \cdot \sec(\theta)}{\cos(\theta) \cdot \tan(\theta)}\\\\[/tex]

The ratio of sine and cosine is equal to tangent, therefore,

[tex]=\dfrac{\tan(\theta) \cdot \sec(\theta)}{ \tan(\theta)}\\\\[/tex]

= sec(θ)

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