Løs frac{sin12^{circ}}{sin12^{circ}}-2/2sin6^circcos6^circ(3-4sin^212^circ)

$$\frac { \sin 12 ^ { \circ } } { \sin 12 ^ { \circ } } - \frac { 2 } { 2 \sin 6 ^ { \circ } \cos 6 ^ { \circ } ( 3 - 4 \sin ^ { 2 } 12 ^ { \circ } ) }$$

Evaluer

$$-\frac{878924782062947310025729862947}{97637717937052689974270137053}\approx -9,001898043$$

Løsningstrinn

Evaluate trigonometric functions in the problem

$$\frac{0,20791169081775931}{0,20791169081775931} - \frac{2}{2 \cdot 0,10452846326765346 \cdot 0,9564956763167232}$$

Del 0,20791169081775931 på 0,20791169081775931 for å få 1.

$$1-\frac{2}{2\times 0,10452846326765346\times 0,9564956763167232}$$

Multipliser 2 med 0,10452846326765346 for å få 0,20905692653530692.

$$1-\frac{2}{0,20905692653530692\times 0,9564956763167232}$$

Multipliser 0,20905692653530692 med 0,9564956763167232 for å få 0,199962046335083909067305240684544.

$$1-\frac{2}{0,199962046335083909067305240684544}$$

Utvid \frac{2}{0,199962046335083909067305240684544} ved å multiplisere både telleren og nevneren med 1000000000000000000000000000000000.

$$1-\frac{2000000000000000000000000000000000}{199962046335083909067305240684544}$$

Forkort brøken \frac{2000000000000000000000000000000000}{199962046335083909067305240684544} til minste felles nevner ved å dele teller og nevner på 2048.

$$1-\frac{976562500000000000000000000000}{97637717937052689974270137053}$$

Konverter 1 til brøk \frac{97637717937052689974270137053}{97637717937052689974270137053}.

$$\frac{97637717937052689974270137053}{97637717937052689974270137053}-\frac{976562500000000000000000000000}{97637717937052689974270137053}$$

Siden \frac{97637717937052689974270137053}{97637717937052689974270137053} og \frac{976562500000000000000000000000}{97637717937052689974270137053} har samme nevner, kan du subtrahere dem ved å subtrahere tellerne.

$$\frac{97637717937052689974270137053-976562500000000000000000000000}{97637717937052689974270137053}$$

Trekk fra 976562500000000000000000000000 fra 97637717937052689974270137053 for å få -878924782062947310025729862947.

$$-\frac{878924782062947310025729862947}{97637717937052689974270137053}$$

Faktoriser

$$-\frac{878924782062947310025729862947}{97637717937052689974270137053} = -9\frac{1,8532062947306434 \times 10^{26}}{9,763771793705269 \times 10^{28}} = -9,001898043434327$$