0

Guest

Courses New

Number of solutions of the equation tan x + sec x = 2 cos x, lying in the interval [0, 2p] is

Number of solutions of the equation tan x + sec x = 2 cos x, lying in the interval [0, 2p] is

Grade:12

2 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
8 years ago
tan x + sec x = 2 cos x
sin x + 1 = 2 cos2x
sin x + 1 = 2 (1 - sin2x)
2 sin2x + sin x - 1 = 0
Solve for sin x:
sin x = - 1, or sin x = 1/2
sin x = -1 means cos x = 0, which is not possible as tan x cant be infinity
Therfore, sin x = 1/2
x = p or x = p - (p / 6), in the interval [0, 2p]
x = p or x = 5p / 6 are the two solutions
Thanks
Bharat Bajaj
IIT Delhi
askiitians faculty
Apptica Corporations
37 Points
8 years ago
2 solutions pi/6 5pi/6

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Algebra

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