Question

if sec theta =a+1/4a then prove that sec theta+tan theta =2a or 1/2a

Answer 1

HELLO DEAR,

Given that:;

secA = x + 1/4x 

we know that:-


1 + tan²A = sec²A 

tan²A = sec²A – 1   

, tan²A = (x + 1/4x)² – 1                
                            
  => x² + 2 × x × 1/4x + 1/16x²-1               
                            
  = > x² + 1/2 + 1/16x² – 1                
                   
   => x²+ 1/16x² – 1/2                 
                           
  => (x – 1/4x)^2 

, tan²A = x – 1/4x or tan²A = - (x – 1/4x) 

put this value of secA and tanA in
the given equation( secA + tanA )

LHS = secA + tanA         
        
         = x + 1/4x + x – 1/4x         
         
         = 2x        
         
          = RHS 

Or 

LHS = secA + tanA        
        
         =x + 1/4x -x + 1/4x          
         
         = 2/4x          
         
         = 1/2x         
        
         = RHS 


I HOPE ITS HELP YOU DEAR,
THANKS