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In the adjoining figure, ABC is a right angled triangle right angled at B; AB = 24 cm and BC = 7 cm. Using the figure answer the question.

In the figure, ABC is a right angled triangle right angled at B; AB = 24 cm and BC = 7 cm. The value of 2 cos A - sin C is? Trigonometrical Ratios, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

The value of 2 cos A - sin C is

  1. 2524\dfrac{25}{24}

  2. 2425\dfrac{24}{25}

  3. 4125\dfrac{41}{25}

  4. 4925\dfrac{49}{25}

Trigonometrical Ratios

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Answer

By formula,

cos A = BaseHypotenuse\dfrac{\text{Base}}{\text{Hypotenuse}}

= ABAC=2425\dfrac{AB}{AC} = \dfrac{24}{25}.

sin C = PerpendicularHypotenuse\dfrac{\text{Perpendicular}}{\text{Hypotenuse}}

= ABAC=2425\dfrac{AB}{AC} = \dfrac{24}{25}.

Substituting value in 2 cos A - sin C we get :

2 cos A - sin C=2×2425−2425=4825−2425=2425.\text{2 cos A - sin C} = 2 \times \dfrac{24}{25} - \dfrac{24}{25} \\[1em] = \dfrac{48}{25} - \dfrac{24}{25} \\[1em] = \dfrac{24}{25}.

Hence, Option 2 is the correct option.

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