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Given that θ = [tex]\frac{\pi}{4}[/tex] , which of the following shows that cosθsecθ = 1?

- [tex](\frac{\sqrt{2} }{2})(\sqrt{2})[/tex]
- [tex](\frac{\sqrt{3} }{2})(2\frac{\sqrt{3}}{3} )[/tex]
- [tex](\frac{{1} }{2})(2)[/tex]

Respuesta :

tramserran

[tex]cos(\frac{\pi }{4}) = \frac{\sqrt{2}}{2}[/tex]   per Unit Circle

[tex]sec(\frac{\pi }{4}) = \frac{1 }{cos(\frac{\pi }{4})} = \frac{1}{\frac{\sqrt{2}}{2}} = \frac{2}{\sqrt{2}} = \frac{2\sqrt{2}}{2}[/tex] = [tex]\sqrt{2}[/tex]

cosθ * secθ = 1

[tex]\frac{\sqrt{2} }{2}[/tex] * [tex]\sqrt{2}[/tex] = 1

               1 = 1

Answer: A

Answer:

Option 1.

Step-by-step explanation:

It is given that

[tex]\theta=\dfrac{\pi}{4}[/tex]

We need to find the expression that shows [tex]\cos \theta\sec \theta=1[/tex].

We know that,

[tex]\cos \left( \dfrac{\pi}{4}\right)=\dfrac{1}{\sqrt{2}}[/tex]

On rationalization, we get

[tex]\cos \left( \dfrac{\pi}{4}\right)=\dfrac{1}{\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{2}}{2}[/tex]

[tex]\sec \left( \dfrac{\pi}{4}\right)=\sqrt{2}[/tex]

Now,

[tex]LHS=\cos \theta\sec \theta[/tex]

[tex]LHS=\left(\dfrac{\sqrt{2}}{2}\right)(\sqrt{2})[/tex]

Therefore, the correct option is 1.

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