Prove that: 4) 2sin²3π/4 + 2cos²π/4 + 2sec²π/3 = 10

Solution:

We know that:

 cos π/4 = 1/√2, sin 3π/4 = 1/√2 and sec π/3 = 2 (by trigonometric table).

Substituting these values in the LHS,

LHS = 2sin²3π/4 + 2cos2π/4 + 2sec²π/3

= 2 × (1/√2)² + 2 × (1/√2)² + 2 × (2)²

= 2 × (1/2) + 2 × (1/2) + 2 × 4

= 1 + 1 + 8

= 10

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 4

Prove that: 4) 2sin²3π/4 + 2cos²π/4 + 2sec²π/3 = 10

Summary:

We got, 2sin²3π/4 + 2cos²π/4 + 2sec²π/3 = 10. Hence Proved