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Q.

If tan(A−B)= tanA−tanB 1+tanA⋅tanB ,   then what could be the value of tan 15 °  ?


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a

3 3 +1  

b

3 +1 3 −1  

c

3 3 −1  

d

3 −1 3 +1   

answer is D.

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Detailed Solution

The given equation is,
tan(A−B)= tanA−tanB 1+tanA.tanB  
Put A= 60 °   and B= 45 ° .  
⇒tan( 60 ° − 45 ° )= tan 60 ° −tan 45 ° 1+tan 60 ° .tan 45 °  
⇒tan 15 ° = 3 −1 1+ 3 ×1  
⇒tan 15 ° = 3 −1 3 +1  
Therefore, the value of tan 15 ° = 3 −1 3 +1 .  
Hence, option (4) is correct.
 
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If tan(A−B)= tanA−tanB 1+tanA⋅tanB ,   then what could be the value of tan 15 °  ?