Tolong bantu nomor 21

2Sin²a + 2Sin a < 3/2
4Sin²a + 4Sina - 3 < 0
(2Sin a - 1)(2Sin a + 3) < 0
-3/2 < Sin a < 1/2

Sin a > -3/2
Tidak memenuhi

Sin a < 1/2
Sin a < Sin 30° , Sin 150°
a < 30° , 150°
a < 1/6 pi
a > 5/6 pi

Gabungkan Hp ny didapat...
Hp : {0 < a < 1/6 pi atau 5/6 pi < a < pi}

[tex]\displaystyle 2\sin^2a+2\sin a\ \textless \ \frac32\\4\sin^2a+4\sin a\ \textless \ 3\\4\sin^2a+4\sin a-3\ \textless \ 0\\4\sin^2a-2\sin a+6\sin a-3\ \textless \ 0\\2\sin a(2\sin a-1)+3(2\sin a-1)\ \textless \ 0\\(2\sin a+3)(2\sin a-1)\ \textless \ 0\\-\frac32\ \textless \ \sin a\ \textless \ \frac12\\\\\sin a\ \textless \ \frac12\\\sin a\ \textless \ \sin\frac16\pi\vee\sin a\ \textless \ \sin\frac56\pi\\a\ \textless \ \frac16\pi\vee a\ \textgreater \ \frac56\pi...\text{HP}_1\\\\\text{syarat }a\\0\ \textless \ a\ \textless \ \pi...\text{HP}_2\\\\\text{HP}=\text{HP}_1\cap\text{HP}_2\\\boxed{\boxed{\text{HP}=\left\{a\left|0\ \textless \ a\ \textless \ \frac16\pi\vee\frac56\pi\ \textless \ a\ \textless \ \pi\right,a\in\mathbb{R}\right\}}}[/tex]