Question

Question 6 Prove that: cos (π / 4 - x).cos (π / 4 - y) - sin (π / 4 - x).sin (π / 4 - y) = sin( x + y )

Class X1 - Maths -Trigonometric Functions Page 73

Answer 1

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

Let ( π/4 -x) = A
(π/4 -y) = B
Then,
LHS = cosA.cosB -sinA.sinB
But we Know,
cos(A + B) = cosA.cosB-sinA.sinB use this,

= cos(A + B)
= cos{(π/4 -x)+(π/4 -y)}
=cos(π/2 -(x +y)}
We know,
Cos(π/2 -∅) = sin∅ use this ,
= sin(x + y) = RHS

Answer 2

Answer:

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

Let ( π/4 -x) = A

(π/4 -y) = B

Then,

LHS = cosA.cosB -sinA.sinB

But we Know,

cos(A + B) = cosA.cosB-sinA.sinB use this,

= cos(A + B)

= cos{(π/4 -x)+(π/4 -y)}

=cos(π/2 -(x +y)}

We know,

Cos(π/2 -∅) = sin∅ use this ,

= sin(x + y) = RHS