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)

Sean O. A Level Physics tutor, IB Physics tutor, GCSE Physics tutor, ...

10 months ago

Answered by Sean, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£22 /hr

Bryan P.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“I am currently a BSc Mathematics student at the University of Bristol and I am already no stranger to teaching.I have worked as a teaching assistant in my secondary school's maths department where I also led one-on-one sessions with ...”

£20 /hr

Noam T.

Degree: Mathematics with Mathematical Physics (Bachelors) - University College London University

Subjects offered: Maths, Physics


“About Myself: I am an undergraduate student at UCL studying Mathematics with Mathematical Physics. Hoping to go into research after my degree, I have a true passion for my subjects and my aim is to pass on that passion to students in ...”

£30 /hr

Thomas D.

Degree: Economics (Bachelors) - Bristol University

Subjects offered: Maths, Geography+ 2 more

Further Mathematics

“Why choose me? I am a highly academic student having achieved 4 A* at A level but also have excellent communication and mentoring skills havingtutored fellow students at school and beenHead Boy. I am honest, reliable and precise, if ...”

About the author

Sean O.

Currently unavailable: until 02/06/2016

Degree: Physics (Masters) - Bristol University

Subjects offered: Maths, Physics


“About me I am a committed and friendly 2nd year physics student at the University of Bristol. The course is intensive in both maths and physics and constantly revisits and reaffirms topics studied at A level. Teaching has always been...”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Find the equation of the tangent to the curve y=x^3-4x^2+2 at the point (3,-7)

How do you integrate e^x cos x

Below is a question from the Edexcel Maths Core 1 textbook, Solve the equation x^2 + 8x + 10 = 0 using completing the square.

How to find y-intercept on a graphical calculator

View A Level Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss