Trignometry

[bharath vb]

[tan225-cot81*cot69]/[cot261+tan21]

plz solve this problem with steps

[shyamjayakannan]

[tex]\frac{\tan{{225}^\circ}-\cot{{81}^\circ}\cot{{69}^\circ}}{\cot{{261}^\circ}+\tan{{21}^\circ}}=\frac{\tan{\left({180}^\circ+{45}^\circ\right)}-\cot{\left({90}^\circ-9^\circ\right)}\cot{\left({90}^\circ-{21}^\circ\right)}}{\cot{\left({270}^\circ-9^\circ\right)}+\tan{{21}^\circ}}=\frac{\tan{{45}^\circ}-\tan{9^\circ}\tan{{21}^\circ}}{\tan{9^\circ}+\tan{{21}^\circ}}=\frac{1-\tan{9^\circ}\tan{{21}^\circ}}{\tan{9^\circ}+\tan{{21}^\circ}}[/tex]

[tex]=\frac{1}{\tan{\left(9^\circ+{21}^\circ\right)}}=\frac{1}{\tan{{30}^\circ}}=\boxed{\sqrt3}[/tex]