Prove the identity: sin^2(x)+cos^2(x) = 1

This is one of the most commonly used A level identities which can be proved using only GCSE maths!

Firstly, take an arbitrary right angle triangle with Hypotenuse h, and angle x between h and the adjacent side. (Diagram recommended)

Label the triangle in terms of h and x using simple SOHCAHTOA:

Hypotenuse = h

Adjacent = hcos(x)

Opposite = hsin(x)

Now, using everyone’s favourite theorem (Pythagorean):

h^2 = h^2cos^2(x)+h^2sin^2(x)

Factoring out h^2 on the right hand side:

h^2 = h^2(cos^2(x)+sin^2(x))

Dividing both sides by h^2 to make it explicit:

1 = cos^2(x)+sin^2(x)

SO
Answered by Sean O. Maths tutor

4316 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do you know how many roots a quadratic equation has?


Is the function f(x)=x^3+24x+3 an increasing or decreasing function?


What is a radian?


The curve C has equation y = x^3 - 3x^2 - 9x + 14. Find the co-ordinates and nature of each of the stationery points of C.


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning