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Q.

State true or false.


tan 60 ° ⋅ cosec 2 45 ° + sec 2 60 ° ⋅tan 45 ° =2 3 +5  


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a

True

b

False 

answer is B.

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Detailed Solution

To check if tan 60 ° ⋅ cosec 2 45 ° + sec 2 60 ° ⋅tan 45 ° =2 3 +5  .
We know that,
cosec 45 ° = 2  ,
sec 60 ° =2  ,
tan 45 ° =1  ,
tan 60 ° = 3  .
Putting the values, we get,
⇒tan 60 ° ⋅ cosec 2 45 ° + sec 2 60 ° ⋅tan 45 ° = 3 × 2 2 + 2 2 ×1  
⇒tan 60 ° ⋅ cosec 2 45 ° + sec 2 60 ° ⋅tan 45 ° =2 3 +4  
⇒tan 60 ° ⋅ cosec 2 45 ° + sec 2 60 ° ⋅tan 45 ° =2 3 +2  
Thus, the correct statement is that tan 60 ° ×cose c 2 45 ° +se c 2 60 ° ×tan 45 ° =2 3 +2  .  Hence, the statement is false.
Thus, option 2 is correct.
 
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