Question

If sec A = x +1/4x
x not equal to 0, find (sec A + tan A).​

Answer 1

Answer:

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

Or

LHS = secA + tanA        

=x + 1/4x -x + 1/4x          

= 2/4x      

= 1/2x

= RHS

Hence proved.

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Answer 2

soln refers to the attachment