Tolong hitung yang nomor satuu.. Disertai caranya ya.. MATERI TRIGONOMETRI KLS X

Bab : Trigonometri
Kelas : X

Identitas Trigonometri:
1). tanα = sinα/cosα
2). secα = 1/cosα
3). (sinα)² + (cosα)² = sin²α + cos²α = 1

Penyelesaian:

[tex] \frac{2(cos60^{o})^{2} +4(sec30^{o})-tan45^{o}}{(sin30^{o})^{2}+(cos30^{o})^{2}} \\ \\ = \frac{2(cos60^{o})^{2} +4( \frac{1}{cos30^{o}} )-\frac{sin45^{o}}{cos45^{o}}}{(sin30^{o})^{2}+(cos30^{o})^{2}} \\ \\ =\frac{2( \frac{1}{2} )^{2} +4( \frac{1}{ \frac{ \sqrt{3} }{2} } )-\frac{ \frac{ \sqrt{2} }{2} }{ \frac{ \sqrt{2} }{2} }}{1} \\ \\ =2( \frac{1}{4} )+4 (\frac{2}{ \sqrt{3} }) -1 \\ \\ = \frac{1}{2} + \frac{8}{ \sqrt{3} } -1 \\ \\ =\frac{1}{2} + \frac{8 \sqrt{3} }{3 } -1 [/tex]

[tex]=\frac{3}{6} + \frac{16 \sqrt{3} }{6 } - \frac{6}{6} \\ \\ =\frac{-3+16 \sqrt{3} }{6 }[/tex]