LHS = tan \(\cfrac{5\pi}4\) cot \(\cfrac{9\pi}4\) + tan \(\cfrac{17\pi}4\) cot \(\cfrac{15\pi}4\)
= tan 225° cot 405° + tan 765° cot 675°
= tan (90° × 2 + 45°) cot (90° × 4 + 45°) + tan (90° × 8 + 45°) cot (90° × 7 + 45°)
We know that when n is odd, cot → tan.
= tan 45° cot 45° + tan 45° [-tan 45°]
= tan 45° cot 45° - tan 45° tan 45°
= 1 × 1 – 1 × 1
= 1 – 1
= 0
= RHS
Hence proved.