ដោះស្រាយ frac{sqrt{3}-tan15^circ}{1+sqrt{3}tan15^circ}

$$\frac { \sqrt { 3 } - \tan 15 ^ { \circ } } { 1 + \sqrt { 3 } \tan 15 ^ { \circ } }$$

វាយតម្លៃ

$$\frac{107179676972449082242158358245529\sqrt{3}-107179676972449080000000000000000}{78460969082652753273524925263413}\approx 1$$

ជំហានចម្លើយ

Evaluate trigonometric functions in the problem

$$\frac{\sqrt{3} - 0.2679491924311227}{1 + \sqrt{3} 0.2679491924311227}$$

ធ្វើសនិទានកម្ម​ភាគបែង​នៃ \frac{\sqrt{3}-0.2679491924311227}{1+0.2679491924311227\sqrt{3}} ដោយគុណ​ភាគយក​ និង​ភាគបែង​​នឹង 1-0.2679491924311227\sqrt{3}។​

$$\frac{\left(\sqrt{3}-0.2679491924311227\right)\left(1-0.2679491924311227\sqrt{3}\right)}{\left(1+0.2679491924311227\sqrt{3}\right)\left(1-0.2679491924311227\sqrt{3}\right)}$$

ពិនិត្យ \left(1+0.2679491924311227\sqrt{3}\right)\left(1-0.2679491924311227\sqrt{3}\right)។ ផលគុណអាចបម្លែងទៅជាផលដកនៃការេដោយប្រើវិធាន៖ \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}។

$$\frac{\left(\sqrt{3}-0.2679491924311227\right)\left(1-0.2679491924311227\sqrt{3}\right)}{1^{2}-\left(0.2679491924311227\sqrt{3}\right)^{2}}$$

គណនាស្វ័យគុណ 1 នៃ 2 ហើយបាន 1។

$$\frac{\left(\sqrt{3}-0.2679491924311227\right)\left(1-0.2679491924311227\sqrt{3}\right)}{1-\left(0.2679491924311227\sqrt{3}\right)^{2}}$$

ពន្លាត \left(0.2679491924311227\sqrt{3}\right)^{2}។

$$\frac{\left(\sqrt{3}-0.2679491924311227\right)\left(1-0.2679491924311227\sqrt{3}\right)}{1-0.2679491924311227^{2}\left(\sqrt{3}\right)^{2}}$$

គណនាស្វ័យគុណ 0.2679491924311227 នៃ 2 ហើយបាន 0.07179676972449082242158358245529។

$$\frac{\left(\sqrt{3}-0.2679491924311227\right)\left(1-0.2679491924311227\sqrt{3}\right)}{1-0.07179676972449082242158358245529\left(\sqrt{3}\right)^{2}}$$

ការេនៃ \sqrt{3} គឺ 3។​

$$\frac{\left(\sqrt{3}-0.2679491924311227\right)\left(1-0.2679491924311227\sqrt{3}\right)}{1-0.07179676972449082242158358245529\times 3}$$

គុណ 0.07179676972449082242158358245529 និង 3 ដើម្បីបាន 0.21539030917347246726475074736587។

$$\frac{\left(\sqrt{3}-0.2679491924311227\right)\left(1-0.2679491924311227\sqrt{3}\right)}{1-0.21539030917347246726475074736587}$$

ដក​ 0.21539030917347246726475074736587 ពី 1 ដើម្បីបាន 0.78460969082652753273524925263413។

$$\frac{\left(\sqrt{3}-0.2679491924311227\right)\left(1-0.2679491924311227\sqrt{3}\right)}{0.78460969082652753273524925263413}$$

អនុវត្ត​លក្ខណៈបំបែកដោយគុណតួនីមួយៗនៃ \sqrt{3}-0.2679491924311227 នឹងតួនីមួយៗនៃ 1-0.2679491924311227\sqrt{3}។

$$\frac{\sqrt{3}-0.2679491924311227\left(\sqrt{3}\right)^{2}-0.2679491924311227+0.07179676972449082242158358245529\sqrt{3}}{0.78460969082652753273524925263413}$$

ការេនៃ \sqrt{3} គឺ 3។​

$$\frac{\sqrt{3}-0.2679491924311227\times 3-0.2679491924311227+0.07179676972449082242158358245529\sqrt{3}}{0.78460969082652753273524925263413}$$

គុណ -0.2679491924311227 និង 3 ដើម្បីបាន -0.8038475772933681។

$$\frac{\sqrt{3}-0.8038475772933681-0.2679491924311227+0.07179676972449082242158358245529\sqrt{3}}{0.78460969082652753273524925263413}$$

ដក​ 0.2679491924311227 ពី -0.8038475772933681 ដើម្បីបាន -1.0717967697244908។

$$\frac{\sqrt{3}-1.0717967697244908+0.07179676972449082242158358245529\sqrt{3}}{0.78460969082652753273524925263413}$$

បន្សំ \sqrt{3} និង 0.07179676972449082242158358245529\sqrt{3} ដើម្បីបាន 1.07179676972449082242158358245529\sqrt{3}។

$$\frac{1.07179676972449082242158358245529\sqrt{3}-1.0717967697244908}{0.78460969082652753273524925263413}$$