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If sec theta = x + 1/x then prove that sec theta *tan theta = 2x or 1/2x

If sec theta = x + 1/x then prove that sec theta *tan theta = 2x or 1/2x

Grade:10

2 Answers

Vikas TU
14149 Points
5 years ago

We realize that sec2 theta=1+tan2theta 
So tan2theta= (x+1/4x)2-1 
On explaining we get tan2theta=(x-1/4x)2 
So tan theta =(x-1/4x) or - (x-1/4x) 
At the point when tan theta =(x-1/4x), 
sec theta +tan theta= x+1/4x+ x-1/4x=2x 
at the point when tan theta =-(x-1/4x) 
sec theta +tan theta= x+1/4x-x+1/4x=1/2x 
Rishi Sharma
askIITians Faculty 646 Points
2 years ago
Dear Student,
Please find below the solution to your problem.

We realize that sec2 theta=1+tan2theta
So tan2theta= (x+1/4x)2-1
On explaining we get tan2theta=(x-1/4x)2
So tan theta =(x-1/4x) or - (x-1/4x)
At the point when tan theta =(x-1/4x),
sec theta +tan theta= x+1/4x+ x-1/4x=2x
at the point when tan theta =-(x-1/4x)
sec theta +tan theta= x+1/4x-x+1/4x=1/2x

Thanks and Regards

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