Trigonometry> If sec theta = x + 1/x then prove that se...

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

Girindra Sonowal , 8 Years ago

Grade 10

2 Answers

Vikas TU

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

Last Activity: 8 Years ago

Rishi Sharma

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

Last Activity: 5 Years ago