By expressing cos(2x) in terms of cos(x) find the exact value of the integral of cos(2x)/cos^2(x) between the bounds pi/4 and pi/3.

cos(2x)=cos2(x)-sin2(x)=2cos2(x)-1
Therefore:cos(2x)/cos2(x)=(2cos2(x)-1)/cos2(x)=2cos2(x)/cos2(x) - 1/cos2(x)=2 - 1/cos2(x)=2 - sec2(x)
Integral of sec2(x) = tan(x)
Integral of 2 = 2x
[2x - tan(x)] between pi/4 and pi/3
= (2pi/3 - tan(pi/3)) -(pi/2 - tan(pi/4))
= (2pi/3 - sqrt(3)) - (pi/2 - 1)
= pi/6 - sqrt(3) + 1

Answered by Hugo F. Maths tutor

6139 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve the inequality x^2 > 3(x + 6)


How to find the stationary point of y= x^2-108x^(1/2)+16 and determine the nature of the stationary point?


Integrate x^2e^x with respect to x between the limits of x=5 and x=0.


A straight line passes through the point (2,1) and has a gradient of 3. Find the co-ordinates where the line crosses the x and y axes


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences