Lutasin ang frac{5cos0^{circ}-2sin30^{circ}+sqrt{3}cos30^{circ}}{tan30^{circ}*tan60^circ*cos60^circ}+3sin29^circsec61^circ

$$\frac { 5 \cos 0 ^ { \circ } - 2 \sin 30 ^ { \circ } + \sqrt { 3 } \cos 30 ^ { \circ } } { \tan 30 ^ { \circ } \times \tan 60 ^ { \circ } \times \cos 60 ^ { \circ } } + 3 \sin 29 ^ { \circ } \sec 61 ^ { \circ }$$

I-evaluate

$$\frac{25138961131425324844637601292748537216888795473}{1218195377141775000000000000000000000000000000}\approx 20.636230939$$

Maiikling Hakbang sa Solution

Evaluate trigonometric functions in the problem

$$\frac{5 \cos(0) - 2 \sin(30) + \sqrt{3} \cos(30)}{0.3118580165482944} + 3 \cdot 0.48480962024633706 \cdot 2.062665339627314$$

Kunin ang halaga ng \cos(0) mula sa talahanayan ng trigonometric values.

$$\frac{5\times 1-2\sin(30)+\sqrt{3}\cos(30)}{0.3118580165482944}+3\times 0.48480962024633706\times 2.062665339627314$$

I-multiply ang 5 at 1 para makuha ang 5.

$$\frac{5-2\sin(30)+\sqrt{3}\cos(30)}{0.3118580165482944}+3\times 0.48480962024633706\times 2.062665339627314$$

Kunin ang halaga ng \sin(30) mula sa talahanayan ng trigonometric values.

$$\frac{5-2\times \frac{1}{2}+\sqrt{3}\cos(30)}{0.3118580165482944}+3\times 0.48480962024633706\times 2.062665339627314$$

I-multiply ang 2 at \frac{1}{2} para makuha ang 1.

$$\frac{5-1+\sqrt{3}\cos(30)}{0.3118580165482944}+3\times 0.48480962024633706\times 2.062665339627314$$

I-subtract ang 1 mula sa 5 para makuha ang 4.

$$\frac{4+\sqrt{3}\cos(30)}{0.3118580165482944}+3\times 0.48480962024633706\times 2.062665339627314$$

Kunin ang halaga ng \cos(30) mula sa talahanayan ng trigonometric values.

$$\frac{4+\sqrt{3}\times \frac{\sqrt{3}}{2}}{0.3118580165482944}+3\times 0.48480962024633706\times 2.062665339627314$$

Ipakita ang \sqrt{3}\times \frac{\sqrt{3}}{2} bilang isang single fraction.

$$\frac{4+\frac{\sqrt{3}\sqrt{3}}{2}}{0.3118580165482944}+3\times 0.48480962024633706\times 2.062665339627314$$

Para magdagdag o mag-subtract ng mga expression, i-expand ang mga iyon para gawing magkakapareho ang mga denominator ng mga ito. I-multiply ang 4 times \frac{2}{2}.

$$\frac{\frac{4\times 2}{2}+\frac{\sqrt{3}\sqrt{3}}{2}}{0.3118580165482944}+3\times 0.48480962024633706\times 2.062665339627314$$

Dahil may parehong denominator ang \frac{4\times 2}{2} at \frac{\sqrt{3}\sqrt{3}}{2}, pagsamahin ang mga ito sa pamamagitan ng pagsasama sa mga numerator ng mga ito.

$$\frac{\frac{4\times 2+\sqrt{3}\sqrt{3}}{2}}{0.3118580165482944}+3\times 0.48480962024633706\times 2.062665339627314$$

Gawin ang mga pag-multiply sa 4\times 2+\sqrt{3}\sqrt{3}.

$$\frac{\frac{8+3}{2}}{0.3118580165482944}+3\times 0.48480962024633706\times 2.062665339627314$$

Kalkulahin ang 8+3.

$$\frac{\frac{11}{2}}{0.3118580165482944}+3\times 0.48480962024633706\times 2.062665339627314$$

Ipakita ang \frac{\frac{11}{2}}{0.3118580165482944} bilang isang single fraction.

$$\frac{11}{2\times 0.3118580165482944}+3\times 0.48480962024633706\times 2.062665339627314$$

I-multiply ang 2 at 0.3118580165482944 para makuha ang 0.6237160330965888.

$$\frac{11}{0.6237160330965888}+3\times 0.48480962024633706\times 2.062665339627314$$

I-expand ang \frac{11}{0.6237160330965888} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 10000000000000000.

$$\frac{110000000000000000}{6237160330965888}+3\times 0.48480962024633706\times 2.062665339627314$$

Bawasan ang fraction \frac{110000000000000000}{6237160330965888} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 128.

$$\frac{859375000000000}{48727815085671}+3\times 0.48480962024633706\times 2.062665339627314$$

I-multiply ang 3 at 0.48480962024633706 para makuha ang 1.45442886073901118.

$$\frac{859375000000000}{48727815085671}+1.45442886073901118\times 2.062665339627314$$

I-multiply ang 1.45442886073901118 at 2.062665339627314 para makuha ang 2.99999999999999987246512207937052.

$$\frac{859375000000000}{48727815085671}+2.99999999999999987246512207937052$$

Idagdag ang \frac{859375000000000}{48727815085671} at 2.99999999999999987246512207937052 para makuha ang \frac{25138961131425324844637601292748537216888795473}{1218195377141775000000000000000000000000000000}.

$$\frac{25138961131425324844637601292748537216888795473}{1218195377141775000000000000000000000000000000}$$