Unconventional Mathematics I

〖cos〗^2 θ+〖sin〗^2 θ=1

〖cos〗^2 (180)+〖sin〗^2 (180)=1

〖(-1)〗^2+〖(0)〗^2=1

1+0=1

1=1, This trigonometric equation checks out

〖cos〗^2 θ+〖sin〗^2 θ=1

〖cos〗^2 θ+〖sin〗^2 θ=sinθ/sinθ

Note: sinθ/sinθ = 1

〖cos〗^2 (180)+〖sin〗^2 (180)=sin〖(180)〗/sin〖(180)〗

〖(-1)〗^2+〖(0)〗^2=1, but this can also be written as:

〖(-1)〗^2+〖(0)〗^2=0/0, because sin (180) = 0.

∴1=0/0

According to the sine function graph, every 180 degree curve sine equals zero, thus creating an infinite number of solutions and proofs for the theory that zero divided by zero equals one. With this assumption a formula had to be within reach. This formula is:

〖cos〗^2 (180K)+〖sin〗^2 (180K)=(sin(180K))/(sin(180K))∎

Where K=1, 2, 3, 4…a_0n In essence all whole, real, and rational numbers check out

K=∈R→[-∞,∞]

This equation is also proportional as can be seen:

(〖cos〗^2 (180K)+〖sin〗^2 (180K))/1∝(sin(180K))/(sin(180K))

〖cos〗^2 θ+〖sin〗^2 θ=sinθ/sinθ Note:(≡〖cos〗^2 θ+〖sin〗^2 θ=1)

sinθ (〖cos〗^2 θ+〖sin〗^2 θ)=sinθ

〖cos〗^2 θ sinθ+〖sin〗^3 θ=sinθ

〖cos〗^2 180 sin180+〖sin〗^3 180= sin180

〖(-1)〗^2×(0)+〖(0)〗^3=0

0+0=0

0=0, as seen this equation checks out as well

〖cos〗^2 θ+〖sin〗^2 θ=sinθ/sinθ

sinθ (〖cos〗^2 θ+〖sin〗^2 θ)=sinθ

〖cos〗^2 θ sinθ+〖sin〗^3 θ=sinθ

With the constant (K) being multiplied by theta, the solution is not effected. As seen below:

θ=180

〖cos〗^2 (180K)+〖sin〗^2 (180K)=(sin(180K))/(sin(180K))

(sin〖180K)〗 (〖cos〗^2 180K+〖sin〗^2 180K)=sin180K

(〖cos〗^2 180K)(sin〖180K)〗+(〖sin〗^2 180K)(sin〖180K)〗=sin180K

(〖cos〗^2 180K)(sin〖180K)〗+(〖sin〗^3 180K)=sin180K

The Proof

〖cos〗^2 (180K)+〖sin〗^2 (180K)=sin(180K)/sin(180K)

Note: 〖cos〗^2 (180K)+〖sin〗^2 (180K)=1 and

sin(180K)/sin(180K) =1

∴1=1∎, this formula/equation proves to be significant

By Arsan Yakubov

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