# Prove that: 2. 2sin^{2}π/6 + cosec^{2}7π/6 cos^{2}π/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 sin^{2}π/6 + cosec^{2}7π/6 cos^{2}π/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. 2sin^{2}π/6 + cosec^{2}7π/6 cos^{2}π/3 = 3/2

**Summary:**

We got, 2sin^{2}π/6 + cosec^{2}7π/6 cos^{2}π/3 = 3/2. Hence Proved.

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