Prove that: 3) cot²π/6 + cosec 5π/6 + 3tan²π/6 = 6

Solution:

We know that:

 cos π/6 = √3, cosec 5π/6 = 2 and tan π/6 = 1/√3 (by trigonometric table).

Substituting these values in the LHS,

LHS = cot²π/6 + cosec 5π/6 + 3tan²π/6 = 6

= (√3)² + 2 + 3 × (1/√3)²

= 3 + 2 + [3 × (1/3)]

= 3 + 2 + 1

= 6

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 3

Prove that: 3) cot²π/6 + cosec 5π/6 + 3tan²π/6 = 6

Summary:

We got, cot²π/6 + cosec 5π/6 + 3tan²π/6 = 6. Hence Proved.