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In ΔABC, AB = 20 cm, BC = 21 cm and AC = 29 cm. What is the value of cot C + cosec C - 2tan A?

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SSC CGL 2020 Tier-I Official Paper 5 (Held On : 16 Aug 2021 Shift 2)
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  1. \(\frac{3}{5}\)
  2. \(\frac{9}{20}\)
  3. \(\frac{2}{5}\)
  4. \(\frac{7}{20}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{2}{5}\)
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Detailed Solution

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Given:

AB = 20 cm

BC = 21 cm 

AC = 29 cm

Concept used:

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

Calculation:

SSC CGL 2017 18th feb 50 1 Hindi hrev images Q13

Using pythagoras theorem,

AC2 = AB2 + BC2

⇒ 292 = 202 + 212

ΔABC is a right angled triangle.

⇒ cot C = BC/AB = 21/20

⇒ cosec C = AC/AB = 29/20

⇒ tan A = BC/AB = 21/20

cot C + cosec C - 2tan A = 21/20 + 29/20 - 2 × 21/20

⇒ 8/20

⇒ 2/5

So, the value of cot C + cosec C - 2tan A = 2/5

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