Question

prove that tan 225 ×cot 405+tan 675×cot315= 2​

Answer 1

Step-by-step explanation:

$tan \: 225 \degree \times cot \: 405 \degree + tan \: 675 \degree \times cot \: 315 \degree = 2 \\ LHS = tan \: 225 \degree \times cot \: 405 \degree\\ + tan \: 675 \degree \times cot \: 315 \degree \\ = tan(180\degree + 45\degree) \times cot(360\degree + 45\degree) \\ + tan(2 \times 360\degree - 45\degree) \times cot(360\degree - 45\degree) \\ = tan \: 45\degree \times cot \: 45\degree + ( - tan \: 45\degree) \times( - cot \: 45\degree ) \\ = 1 \times 1 + ( - 1) \times ( - 1) \\ = 1 + 1 \\ = 2 \\ = RHS \\ Thus \: Proved \\\\</p><p>\because tan(180\degree +\theta) =tan\theta\\tan(360\degree +\theta) =tan\theta\\tan(360\degree - \theta) =-tan\theta\\</p><p>cot(180\degree +\theta) =cot\theta\\cot(360\degree +\theta) =cot\theta\\cot(360\degree - \theta) =-cot\theta</p><p>$