Selesaikan (2)cos80^circ/sin20^circ+cos59^circcsc31^circ=2

$$( 2 ) \frac { \cos 80 ^ { \circ } } { \sin 20 ^ { \circ } } + \cos 59 ^ { \circ } \csc 31 ^ { \circ } = 2$$

Tentu sahkan

Langkah Penyelesaian

Evaluate trigonometric functions in the problem

$${(2)} \frac{0.17364817766693041}{0.3420201433256687} + 0.5150380749100543 \cdot 1.9416040264103567 = 2$$

Kembangkan \frac{0.17364817766693041}{0.3420201433256687} dengan mendarabkan kedua-dua pengangka dan penyebut dengan 100000000000000000.

$$2\times \frac{17364817766693041}{34202014332566870}+0.5150380749100543\times 1.9416040264103567=2$$

Nyatakan 2\times \frac{17364817766693041}{34202014332566870} sebagai pecahan tunggal.

$$\frac{2\times 17364817766693041}{34202014332566870}+0.5150380749100543\times 1.9416040264103567=2$$

Darabkan 2 dan 17364817766693041 untuk mendapatkan 34729635533386082.

$$\frac{34729635533386082}{34202014332566870}+0.5150380749100543\times 1.9416040264103567=2$$

Kurangkan pecahan \frac{34729635533386082}{34202014332566870} kepada sebutan terendah dengan mengeluarkan dan membatalkan 2.

$$\frac{17364817766693041}{17101007166283435}+0.5150380749100543\times 1.9416040264103567=2$$

Darabkan 0.5150380749100543 dan 1.9416040264103567 untuk mendapatkan 1.00000000000000034155305447936881.

$$\frac{17364817766693041}{17101007166283435}+1.00000000000000034155305447936881=2$$

Tukar nombor perpuluhan 1.00000000000000034155305447936881 kepada pecahan \frac{100000000000000034155305447936881}{10000000000}. Kurangkan pecahan \frac{100000000000000034155305447936881}{10000000000} kepada sebutan terendah dengan mengeluarkan dan membatalkan 1.

$$\frac{17364817766693041}{17101007166283435}+\frac{100000000000000034155305447936881}{100000000000000000000000000000000}=2$$

Gandaan sepunya terkecil 17101007166283435 dan 100000000000000000000000000000000 ialah 342020143325668700000000000000000000000000000000. Tukar \frac{17364817766693041}{17101007166283435} dan \frac{100000000000000034155305447936881}{100000000000000000000000000000000} kepada pecahan dengan penyebut 342020143325668700000000000000000000000000000000.

$$\frac{347296355333860820000000000000000000000000000000}{342020143325668700000000000000000000000000000000}+\frac{342020143325668816818024646353650179265047173247}{342020143325668700000000000000000000000000000000}=2$$

Oleh kerana \frac{347296355333860820000000000000000000000000000000}{342020143325668700000000000000000000000000000000} dan \frac{342020143325668816818024646353650179265047173247}{342020143325668700000000000000000000000000000000} mempunyai penyebut yang sama, tambahkan dengan menambahkan pengangka.

$$\frac{347296355333860820000000000000000000000000000000+342020143325668816818024646353650179265047173247}{342020143325668700000000000000000000000000000000}=2$$

Tambahkan 347296355333860820000000000000000000000000000000 dan 342020143325668816818024646353650179265047173247 untuk dapatkan 689316498659529636818024646353650179265047173247.

$$\frac{689316498659529636818024646353650179265047173247}{342020143325668700000000000000000000000000000000}=2$$

Tukar 2 kepada pecahan \frac{684040286651337400000000000000000000000000000000}{342020143325668700000000000000000000000000000000}.

$$\frac{689316498659529636818024646353650179265047173247}{342020143325668700000000000000000000000000000000}=\frac{684040286651337400000000000000000000000000000000}{342020143325668700000000000000000000000000000000}$$

Bandingkan \frac{689316498659529636818024646353650179265047173247}{342020143325668700000000000000000000000000000000} dengan \frac{684040286651337400000000000000000000000000000000}{342020143325668700000000000000000000000000000000}.

$$\text{false}$$