The smallest possible root of the equation tan x = x lies in which interval?? Q3 above
Sandipkumar , 6 Years ago
Grade 11
Trigonometry> The smallest possible root of the equatio...
2 AnswersArun
Last Activity: 6 Years ago
Note that tan x > x in (0, pi/2). It is clear from the graph that the point of intersection lies in the interval (pi/2, 3pi/2) which corresponds to the smallest positive root of tan x - x = 0.
Regards
Arun (askIITians forum expert)
Aditya Gupta
Last Activity: 6 Years ago
consider f(x)= tanx – x
now f ’(x)= sec^2x – 1= tan^2x>=0
now, f(0)=0 so f(x)>0 for all x in (0, π/2)
now, in (π/2. π), f(x) is always negative.
now, f(π)= – π and lim x----> 3π/2- (f(x))= plus infinty
since f(x) is continuous in (π, 3π/2), it has to pass through zero inside this interval
so the smallest positive root lies in (π, 3π/2). option (c)
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on trigonometry
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available
Last Activity: 2 Years ago
Find the general solution of equation tan3∂=cot2∂For all angles between -720 and +720
trigonometry
0 Answer Available
Last Activity: 2 Years ago
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
0 Answer Available
Last Activity: 2 Years ago
cos^2 13ºcos^2 47º+cos^2 73º =? …..................
trigonometry
0 Answer Available
Last Activity: 2 Years ago
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
0 Answer Available
Last Activity: 2 Years ago