0

Guest

Courses New

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
6 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
3 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

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More