Question

tan255 cot405+ tan765 cot675=0

Answer 1

Step-by-step explanation:

Let us consider the LHS:

tan 225° cot 405° + tan 765° cot 675°

tan (90° × 2 + 45°) cot (90° × 4 + 45°) + tan (90°

× 8 + 45°) cot (90° × 7 + 45°)

As 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

∴ LHS = RHS

Thus proved