Prove the following: cos(π/4 - x) cos(π/4 - y) - sin(π/4 - x) sin(π/4 - y) = sin(x+y)

Solution:

LHS = cos (π/4 - x) cos(π/4 - y) - sin (π/4 - x) sin(π/4 - y)

= cos (π/4 - x + π/4 - y) (Using the sum and difference identities, cos x cos y - sin x sin y = cos (x + y))

= cos (π/2 - (x+y))

= sin(x + y)     [Using cofunction identities, cos(π/2 - A) = sin A]

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 6

Prove the following: cos(π/4 - x) cos(π/4 - y) - sin(π/4 - x) sin(π/4 - y) = sin(x+y)

Summary:

We got, cos(π/4 - x) cos(π/4 - y) - sin(π/4 - x) sin(π/4 - y) = sin(x+y). Hence Proved.