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Q.

What is the value of cos 30 ° cos 45 ° sin 30 ° sin 45 °  ?


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a

2 3 1 4  

b

2 3 +1 4  

c

3 2 1 4  

d

2 3 +1 3    

answer is A.

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Detailed Solution

Given expression is cos 30 ° ×cos 45 ° sin 30 ° ×sin 45 °  .
We know that,
cos 30 ° = 3 2  
cos 45 ° =sin 45 ° = 1 2  
sin 30 ° = 1 2  
Putting the values, we get,
cos 30 ° ×cos 45 ° sin 30 ° ×sin 45 ° = 3 2 × 1 2 1 2 × 1 2  
cos 30 ° ×cos 45 ° sin 30 ° ×sin 45 ° = 1 2 3 2 1 2  
Taking LCM, we get,
cos 30 ° ×cos 45 ° sin 30 ° ×sin 45 ° = 1 2 3 1 2   cos 30 ° ×cos 45 ° sin 30 ° ×sin 45 ° = 3 1 2 2  
Rationalizing the denominator, we get,
cos 30 ° ×cos 45 ° sin 30 ° ×sin 45 ° = 3 1 2 2 × 2 2   cos 30 ° ×cos 45 ° sin 30 ° ×sin 45 ° = 2 3 1 4   Thus, the value of cos 30 ° ×cos 45 ° sin 30 ° ×sin 45 °   is 2 3 1 4  .
Hence, option 1 is correct.
 
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