Prove that (1-cos2x)/sin(2x) = tan(x) where x ≠ nπ/2

Starting from the left hand side we can substitute the sin and cos sum and difference formulas. These are sin(A+B) = sinAcosB + cosAsinBand cos(A+B) = cosAcosB - sinAsinBBecause x = A = B when substituted these formulae become:sin(2x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x)cos(2x) = cos2(x) - sin2(x) When substituted into the question(1-cos2(x) + sin2(x))/2sin(x)cos(x) = 2sin2(x)/2sin(x)cos(x) = sin(x)/cos(x) = tan(x)This is as required

Answered by Jed B. Maths tutor

8375 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the area encompassed by y=(3-x)x^2 and y=x(4-x) between x=0 and x=2.


How can you find the coefficients of a monic quadratic when you know only one non-real root?


Differentiate the function f(x) = x*sin(x)


The graphs of functions f(x)=e^x and h(x)=e^(-.5x), where x is a real number and 0<x<1 ,lie on a plane. Draw these functions and find the area they and the line x=0.6 enclose using integration correct to 3 decimal places


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