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

4128 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Use the substition u = cos(x) to find the indefinite integral of -12sin(x)cos^3(x) dx


For the curve f(x) = 2x^3 - 54x, find the stationary points and state the nature of these points


Explain how Differentiation by the chain rule works


Solve the differential equation dy/dx=(y^(1/2))*sin(x/2) to find y in terms of 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