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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 tan A + cot C is? Trigonometrical Ratios, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

The value of tan A + cot C is

  1. 712\dfrac{7}{12}

  2. 127\dfrac{12}{7}

  3. 1425\dfrac{14}{25}

  4. 2512\dfrac{25}{12}

Trigonometrical Ratios

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Answer

By formula,

tan A = PerpendicularBase\dfrac{\text{Perpendicular}}{\text{Base}}

= BCAB=724\dfrac{BC}{AB} = \dfrac{7}{24}.

cot C = BasePerpendicular\dfrac{\text{Base}}{\text{Perpendicular}}

= BCAB=724\dfrac{BC}{AB} = \dfrac{7}{24}.

Substituting value in tan A + cot C we get :

tan A + cot C=724+724=1424=712.\text{tan A + cot C} = \dfrac{7}{24} + \dfrac{7}{24} \\[1em] = \dfrac{14}{24} \\[1em] = \dfrac{7}{12}.

Hence, Option 1 is the correct option.

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