0
$\begingroup$

How to solve system of three trigonometric equations:

$(\sin x)^2 (\cos y)^2 = 4 \cos x \sin y\tag1$

$(\sin y)^2 (\cos z)^2 = 4 \cos y \sin z \tag2$

$1- \sqrt{\sin z}(1+\sqrt{\cos x})=\sqrt{\frac{1-\sin y}{1+\sin y}}\tag3$

and to verify that

$\sin x=\sqrt{2}(\sqrt{2}+1)\sqrt{\sqrt{10}-3}(\sqrt{5}-2)\\ \sin y=(\sqrt{2}-1)^2(\sqrt{10}-3)\\ \sin z=(2\sqrt{2}+\sqrt{5}-\sqrt{12+4\sqrt{10}})^2(\sqrt{5}+\sqrt{2}-\sqrt{6+2\sqrt{10}})^2$

not is the only solution, but that many others exist?

  • 0
    from where comes this system? – 2017-01-24
  • 0
    i there a bracket missing in the third equation? – 2017-01-24
  • 0
    I beg your pardon. In eqn. (3) it is correct $\cos x$ and not $\cos z$. – 2017-01-25

0 Answers 0