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(*) If tan b =( n tan a ) / 1 + (1-n) tan square a, then tan (a-b) =

(*)
If tan b =( n tan a ) / 1 + (1-n) tan square a, then tan (a-b) =

Grade:11

1 Answers

varad pawar
21 Points
6 years ago
tanA-B= tanA-tanB                      { by substituting the value of tanB we get }
             1+tanAtanB        
 
=tanA -    NtanA    
             1+(1-N)tan2A       {by cross multiplication we get }
1 -   tanA × NtanA      
        1+(1-N)tan2a
 
= tanA+tan3A-Ntan3A-NtanA 
                1+(1-N)tan2A              
   1+tan2A-Ntan2A+Ntan2A   
                1+(1-N)tan2A
 
= tanA+tan3A-Ntan3A-NtanA   ×          1+(1-N)tanA        
               1+(1-N)tanA                            1+tan2A
 
=  tanA-NtanA+tan3A-Ntan3A    …...{ now by taking tanA and N as comman we get }
                   1+tan2A
 
=  (1-N)tanA + (1-N)tan3A    …..{ now by taking (1-N)tanA as comman we get }
                1+tan2A
 
= (1-N)tanA A }2{ 1+tan
              ​A21+tan
 
Ans =    (1-N)tanA     
 
 

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