Q.

What is the value of sin 45 ° cos 45 ° sin 2 30 °  ?


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a

1 4  

b

1 2  

c

1 3  

d

0  

answer is A.

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Detailed Solution

We have to find the value of sin 45 ° cos 45 ° sin 2 30 °  .
We know that,
sin 45 ° = 1 2    cos 45 ° = 1 2  
sin 30 ° = 1 2  
Putting the value of trigonometric functions for given angles in the expression sin 45 ° .cos 45 ° sin 2 30 °  , we get,
sin 45 ° cos 45 ° sin 2 30 ° = 1 2 . 1 2 1 2 2   sin 45 ° cos 45 ° sin 2 30 ° = 1 2 1 4   sin 45 ° cos 45 ° sin 2 30 ° = 21 4    sin 45 ° cos 45 ° sin 2 30 ° = 1 4   Thus, the value of sin 45 ° cos 45 ° sin 2 30 °   is 1 4  .
Hence, option 1 is correct.
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