Question

Prove: $\tan {225}^o\cot {405}^o+\tan {765}^o=2$

Answer 1

To prove,

$\tan {225}^o\cot {405}^o+\tan {765}^o=2$

$\tan {225}^o=\tan ({180}^o+{45}^o)$

$=\tan {45}^o$

$\tan {45}^o=1$

$\cot {405}^o=\cot ({360}^o-{45}^o)$

$=\cot {45}^o$

$\cot {45}^o=1$

$\tan {765}^o=\tan ({720}^o+{45}^o)$

$=\tan {45}^o$

$\tan {45}^o=1$

$\therefore \tan {225}^o\cot {405}^o+\tan {765}^o$

$=1\times 1+1$

$=2$.