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What is the value of cos 18° - sin 18° ? 
1. √2 sin27° 
2. \(\rm 1 \over \sqrt 2\)sin27° 
3. √2 cos27° 
4. \(\rm 1 \over \sqrt 2\)cos27° 

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Correct Answer - Option 1 : √2 sin27° 

Concept:

cos (90 - x) = sin x

sin A - sin B = 2cos\(\rm (A+B) \over 2\)sin \(\rm (A-B) \over 2\)

cos 45° = \(1 \over \sqrt 2\)

 

Calculation:

Given,

cos18° - sin18°

= cos (90° - 72°) - sin 18°

= sin 72° - sin 18°

= 2 cos \(\rm (72°+18°) \over 2\)× sin \(\rm (72°-18°) \over 2\)

= 2 cos 45° sin 27°

= 2× \(1 \over \sqrt 2\)× sin 27°

= √2 sin 27° 

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