Question

To prove :
Cos(x+y) * cos(x-y) = cos square y - sin square x

Answer 1

Answer:

Step-by-step explanation:

L.H.S:

[cos(x)cos(y)–sin(x)sin(y)] [cos(x)cos(y)+sin(x)sin(y)]

= cos²(x)cos²(y) - sin²(x)sin²(y)

= cos²(x)cos²(y) - [(1-cos²(x))(1-cos²(y))]

= cos²(x)cos²(y) - (1-cos²(x) - cos²(y) + cos²(x)cos²(y)]

= cos²(x)cos²(y) - 1 + cos²(x) + cos²(y) - cos²(x)cos²(y)

= cos²(y)  - (1 - cos²(x))

= cos²(y) - sin²(x)

= R.H.S