Show that (sec(x))^2 /(sec(x)+1)(sec(x)-1) can be written as (cosec(x))^2.

( sec2(x))/((sec(x)+1)(sec(x)-1))Then, by the rule of 'difference of two squares', we know that this equals= (sec2(x))/(sec2(x)-1)= (sec2x/tan2x)since 1+tan2(x)=sec2(x), we get sec2(x)-1=tan2(x). By multiplying throughout by cos2(x), we get(sec2x/tan2x)=1/sin2(x)=cosec2(x)as required.

Answered by Rishi S. Maths tutor

10350 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Using Discriminants to Find the Number of Roots of a Quadratic Curve


Find the tangent to the curve y=x^2 +2x at point (1,3)


solve the differential equation dy/dx=(3x*exp(4y))/(7+(2x^(2))^(2) when y = 0, x = 2


Solve the following integral: ∫ arcsin(x)/sqrt(1-x^2) dx


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