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Mathematics

If sec θ = (257)\Big(\dfrac{25}{7}\Big), then the value of cot θ is:

  1. (2524)\Big(\dfrac{25}{24}\Big)

  2. (247)\Big(\dfrac{24}{7}\Big)

  3. (724)\Big(\dfrac{7}{24}\Big)

  4. (2425)\Big(\dfrac{24}{25}\Big)

Trigonometric Identities

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Answer

sec θ = (257)=hypotenusebase\Big(\dfrac{25}{7}\Big) = \dfrac{\text{hypotenuse}}{\text{base}}

Perpendicular = 25272=576\sqrt{25^2 - 7^2} = \sqrt{576} = 24.

cot θ = Baseperpendicular=(724)\dfrac{\text{Base}}{\text{perpendicular}} = \Big(\dfrac{7}{24}\Big).

Hence, option 3 is the correct option.

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