Prove that the d(tan(x))/dx is equal to sec^2(x).

You can express tan(x) as sin(x)/cos(x). Therefore, tan(x)= sin(x)/ cos(x)The quotient rule can be applied here as there is a function of x in the numerator and denominator.Quotient Rule: (v*(du/dx) - u*(dv/dx))/v2Let u =sin(x) and v=cos(x) and hence (du/dx)= cos(x) and (dv/dx)= -sin(x).Therefore:d(tan(x))/dx= (cos(x)cos(x))-(sin(x)(-sin(x))/(cos2(x))=(cos2(x)+sin2(x))/(cos2(x))Using the trig identity, cos2(x)+sin2(x)=1, the numerator of the fraction can be tidied and heavily simplified.d(tan(x))/dx= 1/(cos2(x))As 1/(cos(x)) is equal to sec(x), 1/(cos2(x)) is equal to sec2(x).

CU
Answered by Chinazam U. Maths tutor

17666 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Write tan(3x) in terms of tan(x). Hence show that the roots of t^3 - 3t^2 - 3t + 1 = 0 are tan(pi/12), tan(5pi/12) and tan(3pi/4)


A Block of mass 2kg is on an a smooth inclined plane where sin@ = 3/5 at point A. Point B is 5 meters down the incline. Find the time it will take for the block to reach point given it is at rest at point A.


A line L is parallel to y = 4x+5 and passes through the point (-1,6). Find the equation of the line L in the form y = ax+b.


œintegrate xe4x in respect to x


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