Question

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$\mathfrak{if sec theta = x + 1x/4, prove that sec theta + tan theta = 2x or 1/2x}$

Answer 1

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QUESTION :)






tex]\mathfrak{if sec theta = x + 1x/4, prove that sec theta + tan theta = 2x or 1/2x}[/tex]



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ANSWERS :)






Solution - 

Given – 
secA = x + 1/4x 

As 1 + tan^2A = sec^2A 

tan^2A = sec^2A – 1   

Therfore, tan^2A = (x + 1/4x)^2 – 1                
                            
                            = x^2 + 2*x*1/4x + 1/16x^2 – 1               
                            
                            = x^2 + 1/2 + 1/16x2 – 1                
                            
                            = x^2 + 1/16x^2 – 1/2                 
                           
                            = (x – 1/4x)^2 

Therefore, tan^2A = x – 1/4x or tan^2A = - (x – 1/4x) 

Substitute the value of secA and tanA in the given equation secA + tanA 

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



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


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Answer 2

Answer:

$</p><p>[tex]\mathfrak{if sec theta = x + 1x/4, prove that sec theta + tan theta = 2x or 1/2x}$[/tex]

past few days ago and