Prove that 1 + tan^2 x = sec^2 x

We know that tan x = sin x/cos x and so tan2x = sin2x/cos2x. We also know that sin2x + cos2x = 1 because this is a Pythagorean identity. We can rewrite the left hand side as (cos2x + sin2x)/cos2x because 1 can be rewritten as cos2x/cos2x. Because sin2x + cos2x = 1, we can simplify the numerator of the left hand side, meaning that  (cos2x + sin2x)/cos2x  = 1/cos2x  which is sec2x (the right hand side). Therefore LHS=RHS and we have proven 1 + tan2 x = sec2 x

EF
Answered by Eleanor F. Maths tutor

15958 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The complex numbers Z and W are given by Z=3+3i and W=6-i. Giving your answers in the form of x+yi and showing how you clearly obtain them, find: i) 3Z-4W ii) Z*/W


A curve (C) with equation y=3x^(0.5)-x^(1.5) cuts the X axis at point A and the origin, calculate the co-ordinates of point A.


Where does the quadratic formula come from?


Find the indefinite integral of cos^2 x


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences