# Easy derivation of pythagorean trigonometric identities

Let's derive the equation sin2x + cos2x=1 from the pythagorean formula.

A right triangle with angle x will have a leg that is adjacent to angle x and it will have a leg that is opposite to angle x.  There will also be a hypotenuse.

From trigonometry, a right triangle with a given angle x,  can defined as follows:
opposite/hypotenuse=sinx

Following is the pythagorean identity for our right triangle:

If we divide the above equation by hypotenuse2, we have:

Substitute in sinx and cosx into the above equation:

cos2x+sin2x=1

Can you derive the other two Pythagorean trigonometric identities?

cot2x + 1=csc2x
tan2x  + 1=sec2x

Hint:  These can be derived by using the same right triangle that we used above or these can be derived by dividing cos2x+sin2x=1 by either sin2x or cos2x.

Now you don't need to remember these equations for your trig identity test.  You can derive these yourself! \$68p/h

Benjamin E.

Experience Math and Science educator

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