kelas : XI SMA mapel ; matematika kategori : trigonometri soal: diketahui: sinX.cosX = 8/25 ditanya: nilai dari 1/sinX - 1/cosX = ....?

[tex] \frac{1}{ \sin(x) } - \frac{1}{ \cos(x) } = \frac{ \cos(x) - \sin(x) }{ \sin(x) \cos(x) } = a \\ kuadratin \: kedua \: ruas \\ \frac{{\cos(x) }^{2} + { \sin(x) }^{2} - 2 \sin(x) \cos(x) }{ {( \sin(x) \cos(x)) }^{2} } = {a}^{2} \\ \frac{1 - 2( \frac{8}{25} )}{ {( \frac{8}{25}) }^{2} } = {a}^{2} \\ \frac{1 - \frac {16}{25} }{ \frac{64}{625} } = {a}^{2} \\ \frac{ \frac{9}{25} }{ \frac{64}{625} } = {a}^{2} \\ \frac{25 \times 9}{64} = {a }^{2} \\ a = \frac{5 \times 3}{8} \\ a = \frac{15}{8} \\ jadi \: \frac{1}{ \sin(x) } - \frac{1}{ \cos(x) } = \frac{15}{8} [/tex]