Explicație pas cu pas:
[tex]x\in ( \frac{\pi}{2} ; \pi)[/tex]
cadranul II, semnul: sinx +, cosx -
[tex] \cos(2x) = 2 \cos^{2} (x) - 1 [/tex]
[tex]\iff 2 \cos^{2} (x) - 1 = - \frac{1}{2} \\ 2 \cos^{2} (x) = \frac{1}{2} \iff \cos^{2} (x) = \frac{1}{4} \\ \cos(x) = - \frac{1}{2};\cos(x) = \frac{1}{2} \\[/tex]
x in cadran II
[tex]\implies \cos(x) = - \frac{1}{2} \\ [/tex]
[tex]\cos(2x) = \cos^{2} (x) - \sin^{2} (x)[/tex]
[tex]- \frac{1}{2} = \frac{1}{4} - \sin^{2} (x) \iff \sin^{2} (x) = \frac{1}{2} + \frac{1}{4} = \frac{3}{4} \\ [/tex]
[tex]\sin(x) = - \frac{ \sqrt{3} }{2}, \sin(x) = \frac{ \sqrt{3} }{2}[/tex]
x in cadran II
[tax]\implies \sin(x) = \frac{ \sqrt{3} }{2}[tex] \\
