Prove that: 2. 2sin²π/6 + cosec²7π/6 cos²π/3 = 3/2

Solution:

We know that:

 cos π/3 = 1/2, sin π/6 = 1/2 and cosec 7π/6 = -2 (by trigonometric table).

Substituting these values in the LHS,

LHS = 2 sin²π/6 + cosec²7π/6 cos²π/3

= 2 × (1/2)² + (-2)² × (1/2)²

= 2 × (1/4) + 4 × (1/4)

= (1/2) + 1

= 3/2

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 2

Prove that: 2. 2sin²π/6 + cosec²7π/6 cos²π/3 = 3/2

Summary:

We got, 2sin²π/6 + cosec²7π/6 cos²π/3 = 3/2. Hence Proved.