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

JB
Answered by Jed B. Maths tutor

8492 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

differentiate 4x^3 + 3x


dy/dx of 2x (3x - 1)^5


Integrate 4/x^2


The complex conjugate of 2-3i is also a root of z^3+pz^2+qz-13p=0. Find a quadratic factor of z^3+pz^2+qz-13p=0 with real coefficients and thus find the real root of the equation.


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