(i) LHS = \(\frac{2sin68^\circ}{cos22^\circ}-\frac{2cot15^\circ}{5tan75^\circ}- \frac{3{tan45^\circ}{tan20^\circ}{tan40^\circ}{tan50^\circ}{tan70^\circ}}5\)
= \(\frac{2sin68^\circ}{sin(90^\circ-22^\circ)}-\frac{2cot15^\circ}{5tan75^\circ}- \frac{3\times1\times{cot(90^\circ-20^\circ)}\times{cot(90^\circ-40^\circ)}\times{tan50^\circ}\times{tan70^\circ}}5\)
= \(\frac{2sin68^\circ}{sin68^\circ}-\frac{2cot15^\circ}{5cot15^\circ}- \frac{3\times{cot70^\circ}{tan50^\circ}tan70^\circ}5\)
= 2 - \(\frac{2}5\)- \(\frac{3\times{\frac{1}{tan70^\circ}}\times{\frac{1}{tan50^\circ}}\times{tan50^\circ}\times{tan70^\circ}}5\)
= 2 - \(\frac{2}5\)- \(\frac{3}5\)
= \(\frac{10-2-3}5\)
= \(\frac{5}5\)
= 1
= RHS
(ii) LHS = \(\frac{7cos55^\circ}{3sin35^\circ}-\frac{4(cos70^\circ{cosec20^\circ})}{3(tan5°tan25^\circ{tan45^\circ}tan65^\circ{tan85^\circ})}\)
= \(\frac{7cos55^\circ}{3cos(90^\circ-35^\circ)}-\frac{4(sin(90^\circ-70^\circ)cosec 20^\circ}{{3cot(90^\circ- 5^\circ)}\times{cot(90^\circ-25^\circ)}\times1\times{tan65^\circ}\times{tan85^\circ}}\)
= \(\frac{7cos55^\circ}{3cos55^\circ}\) - \(\frac{{4(sin20^\circ}{cosec20^\circ})}{{3({cot85^\circ}{cot65^\circ}{tan65^\circ}{tan85^\circ}}}\)
= \(\frac{7}3\) - \(\frac{{4(sin20^\circ}\times{\frac{1}{tan20^\circ}})}{{3({\frac{1}{tan85^\circ}}\times{\frac{1}{tan65^\circ}}{tan65^\circ}{tan85^\circ)}}}\)
= \(\frac{7}3\) - \(\frac{4}3\)
= \(\frac{3}3\)
= 1
= RHS
