Selesaikan 1/sin^220^circ-tan^2110^circ

$$\frac { 1 } { \sin ^ { 2 } 20 ^ { \circ } } - \tan ^ { 2 } 110 ^ { \circ }$$

Evaluasi

$$\frac{30128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000}\approx 16,097264341$$

Langkah Solusi

Evaluate trigonometric functions in the problem

$$\frac{1}{0,3420201433256687 ^ {2}} - -2,7474774194546225 ^ {2}$$

Hitung 0,3420201433256687 sampai pangkat 2 dan dapatkan 0,11697777844051095979530830215969.

$$\frac{1}{0,11697777844051095979530830215969}-\left(-2,7474774194546225^{2}\right)$$

Kembangkan \frac{1}{0,11697777844051095979530830215969} dengan mengalikan pembilang dan penyebut dengan 100000000000000000000000000000000.

$$\frac{100000000000000000000000000000000}{11697777844051095979530830215969}-\left(-2,7474774194546225^{2}\right)$$

Hitung 2,7474774194546225 sampai pangkat 2 dan dapatkan 7,54863217041303166704533661750625.

$$\frac{100000000000000000000000000000000}{11697777844051095979530830215969}-\left(-7,54863217041303166704533661750625\right)$$

Kebalikan -7,54863217041303166704533661750625 adalah 7,54863217041303166704533661750625.

$$\frac{100000000000000000000000000000000}{11697777844051095979530830215969}+7,54863217041303166704533661750625$$

Konversikan angka desimal 7,54863217041303166704533661750625 menjadi pecahan \frac{1207781147266085066727253858801}{10000000000}. Kurangi pecahan \frac{1207781147266085066727253858801}{10000000000} ke suku terendah dengan mengekstraksi dan membatalkan 1.

$$\frac{100000000000000000000000000000000}{11697777844051095979530830215969}+\frac{1207781147266085066727253858801}{160000000000000000000000000000}$$

Kelipatan persekutuan terkecil dari 11697777844051095979530830215969 dan 160000000000000000000000000000 adalah 1871644455048175356724932834555040000000000000000000000000000. Ubah \frac{100000000000000000000000000000000}{11697777844051095979530830215969} dan \frac{1207781147266085066727253858801}{160000000000000000000000000000} menjadi pecahan dengan penyebut 1871644455048175356724932834555040000000000000000000000000000.

$$\frac{16000000000000000000000000000000000000000000000000000000000000}{1871644455048175356724932834555040000000000000000000000000000}+\frac{14128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000}$$

Karena \frac{16000000000000000000000000000000000000000000000000000000000000}{1871644455048175356724932834555040000000000000000000000000000} dan \frac{14128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000} memiliki penyebut yang sama, tambahkan bilangan dengan menambahkan pembilangnya.

$$\frac{16000000000000000000000000000000000000000000000000000000000000+14128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000}$$

Tambahkan 16000000000000000000000000000000000000000000000000000000000000 dan 14128355544951823826959762297674094096820918803064623461393169 untuk mendapatkan 30128355544951823826959762297674094096820918803064623461393169.

$$\frac{30128355544951823826959762297674094096820918803064623461393169}{1871644455048175356724932834555040000000000000000000000000000}$$