You can see the pythagorean thereom relationship clearly if you consider the unit circle where the angle is t the opposite side is sin t y the adjacent side is cos t x and the hypotenuse is 1. Note that the three identities above all involve squaring and the number 1.
1 sin 2θ.
Sin2theta identity. Geometrically these are identities involving certain functions of one or more angles they are distinct from triangle identities which are identities potentially involving angles but also. Following table gives the double angle identities which can be used while solving the equations. You can also have sin 2theta cos 2theta expressed in terms of tan theta as under.
In mathematics trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. The two identities labeled a a prime are simply different versions of a. These are called pythagorean identities because as we will see in their proof they are the trigonometric version of the pythagorean theorem.
Sin 2theta 2tan theta 1 tan 2 theta cos 2theta 1 tan 2 theta 1 tan 2 theta.