In ΔXYZ, right angled at Y, if sin X = \(\frac{1}{2}\), find the value of cos X cos Z + sin X sin Z.

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SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 3)
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  1. \(\frac{\sqrt3}{2}\)
  2. \(\frac{\sqrt3}{4}\)
  3. \(\frac{2}{\sqrt3}\)
  4. \(\sqrt3\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{\sqrt3}{2}\)
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Detailed Solution

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Formula used:

cos X cos Z + sin X sin Z = (cos Z - X)

Calculation:

Given that, Y = 90° and

sin X = 1/2 or X = 30° 

We know that 

X + Y + Z = 180° 

30° + 90° + Z = 180°

Z = 60° 

Therefore,

(cos Z - X) = cos (60° - 30°)

cos 30° = √3/2

∴ The correct option is 1

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