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Q.

If the value of sinA= 12 13   then the values of the other trigonometric ratios will be


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a

cosA= 5 13 ,tanA= 12 5 ,cosecA= 13 12 ,secA= 13 5 ,cotA= 5 12  

b

cosA= 5 13 ,tanA= 11 5 ,cosecA= 13 11 ,secA= 12 5 ,cotA= 3 12  

c

cosA= 12 13 ,tanA= 13 5 ,cosecA= 13 5 ,secA= 13 5 ,cotA= 5 12  

d

cosA= 5 13 ,tanA= 12 3 ,cosecA= 13 11 ,secA= 12 5 ,cotA= 11 12   

answer is A.

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Detailed Solution

Given that,
sinA= 12 13   sinA= 12 13 opp hyp = 12 13   We use the Pythagoras theorem,
A C 2 =A B 2 B C 2 A C 2 = 13 2 12 2 A C 2 =25 AC=5 adj=5  
Using the basic trigonometric relations,
cosA= adj hyp = 5 13  
Question Image tanA= opp adj = 12 5  
  cosecA= hyp opp = 13 12  
secA= hyp adj = 13 5   cotA= adj opp = 5 12  
Thus, the other values are cosA= 5 13 ,tanA= 12 5 ,cosecA= 13 12 ,secA= 13 5 ,cotA= 5 12  .
Therefore the correct option is 1.
 
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