Question

sec theta is equal to X + 1 by 4 x then prove that sec theta + 10 theta is equal to 2 x

Answer 1

Hope it helps to solve ur quarry..!

Answer 2

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 .
Hence Proved.