L.H.S. = cot (π/4 – 2cot ⁻¹ 3)

= cot { π/4 – 2 tan ⁻¹ (1/3) } [ As, cot ⁻¹ x = tan ⁻¹(1/x) ]

= cot [ tan ⁻¹ (1) – tan ⁻¹ {(2/3)/(1 – 1/9)} ]

= cot [ tan ⁻¹ (1) – tan ⁻¹ {(2/3)/(8/9)} ]

= cot [ tan ⁻¹ (1) – tan ⁻¹ (3/4) ]

= cot [ tan ⁻¹ {(1 – 3/4)/(1 + 3/4)} ]

= cot [ tan ⁻¹ (1/7) ] 

= cot [ cot ⁻¹ (7) ] = 7 = R.H.S. 

Hence, It's simplest form is 7

Hope it helps :D

Answer:

Step-by-step explanation: