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Q.

tan 2 60 ° +4 cos 2 45 ° +3 sec 2 30 ° +5 cos 2 90 ° cosec 30 ° +sec 60 ° − cot 2 30 ° =  [[1]].


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Detailed Solution

tan 2 60 ° +4 cos 2 45 ° +3 sec 2 30 ° +5 cos 2 90 ° cosec 30 ° +sec 60 ° − cot 2 30 ° =9  .
Given expression is tan 2 60 ° +4 cos 2 45 ° +3 sec 2 30 ° +5 cos 2 90 ° cosec 30 ° +sec 60 ° − cot 2 30 °  .
We know that,
cos 45 ° = 1 2  
sec 30 ° = 2 3  
cosec 30 ° =2  
tan 60 ° =cot 30 ° = 3  
cos 90 ° =0  
sec 60 ° =2  
Substitute the values in the expression and solve,
⇒ 3 2 +4 1 2 2 +3 2 3 2 +5 0 2 2+2− 3 2  
Opening squares, we get,
⇒ 3+4× 1 2 +3× 4 3 +5×0 2+2−3  
⇒ 3+2 4 × 1 2 + 3 × 4 3 +5×0 4−3   ⇒ 3+2+4 1  
⇒9  
Thus, the value of tan 2 60 ° +4 cos 2 45 ° +3 sec 2 30 ° +5 cos 2 90 ° cosec 30 ° +sec 60 ° − cot 2 30 ° =9  .
 
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