Question

Prove that: tan 225° cot 405° + tan 765° cot 675° = 0.

Answer 1

L.H.S.

= tan 225° cot 405° + tan 765° cot 675°

= tan (360° – 135°) cot (360° + 45°) + tan (2 × 360° + 45°) cot (2 × 360° – 45°)

= (- tan 135°) (cot 45°) + (tan 45°) (- cot 45°)

= – tan 135° cot 45° – tan 45° cot 45°

= – tan (180° – 45°) cot 45° – tan 45° cot 45°

= – (- tan 45°) cot 45° – tan 45° cot 45°

= tan 45° cot 45° – tan 45° cot 45° = 0

= R.H.S.

Hence Proved.