Prove that: cot(π/6) + cosec(5π/6) + 3tan(π/6) = 6

LHS=cot(π/6) + cosec(5π/6) + 3tan(π/6) = √3/2 + cosec(π - π/6) + 3(1/√3) = √3/2 + cosec(π/6) + 3/(√3) = √3/2 + 2 + √3 = (√3 + 4 + 2√3)/2 = (4 + 3√3)/2 = (4 + 4.33)/2 = 8.33/2 = 4.165 This is not equal to 6. There is a mistake in either the question or the given solution. Let's re-examine the calculation. LHS = cot(π/6) + cosec(5π/6) + 3tan(π/6) = √3 + cosec(π - π/6) + 3(1/√3) = √3 + cosec(π/6) + √3 = √3 + 2 + √3 = 2 + 2√3 ≈ 2 + 2(1.732) = 2 + 3.464 = 5.464. This is also not equal to 6. Let's assume the question intended to be: cot²(π/6) + cosec(5π/6) + 3tan²(π/6) = 6 Then LHS = (√3)² + 2 + 3(1/√3)² = 3 + 2 + 3(1/3) = 3 + 2 + 1 = 6. Hence proved.