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sin(a+b)/cos(a-b)=1-m/1+m , then prove that tan(45-a)*tan(45-b). Please give the solution with all steps. Thank You

sin(a+b)/cos(a-b)=1-m/1+m , then prove that tan(45-a)*tan(45-b). Please give the solution with all steps.
Thank You
 
 

Grade:11

1 Answers

Sai Rakshit
44 Points
6 years ago
tan(45-a)=1-tan a/1+tan a=(cos a – sin a) / (cos a + sin a) 
tan(45-b)=1-tan b/1+tan b =(cos b – sin b) / (cos b + sin b)
tan(45-a)*tan(45-b)={cos(a-b) – sin (a+b)} / {cos(a-b) + sin (a+b)}
 since,     sin(a+b)/cos(a-b)=1-m/1+m,
   tan(45-a)*tan(45-b) =[ 1-  (1-m/1+m)] / [1+(1-m/1+m ) ]        
                                    = (1+m-1+m) /  (1+m+1-m)    
                                    =  m  Ans. 
   
 
 

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