Question

Prove that cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)=sin(x+y)

Answer 1

Answer:

Step-by-step explanation:

cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)

//using Cos(A+B) = CosACosB - SinASinB

=>  Cos(π/4 - x+ π/4 - y)

=> Cos(2*π/4 - (x+y)]

=> Cos(π/2 - (x+y))

//using Cos(90-θ) = SInθ

=> Sin(x+y)

= R.H.S

Hence proved