Question

The value of
sin((n + 1)A] sin((n + 2)A] + cos((n + 1)A] cos((n + 2)A] is equal to​

Answer 1

Answer:

to prove:-

sin(n+1) x sin(n+2) x+

cos(n+1)xcos(n+2)x=cos x

proof:-

L.H.S

sin(n+1)x sin(n+2)x+

cos(n+1)x cos(n+2)x

= cos((n+2) x—(n-1)x)

= cos ((n+2-n-1)x) {•.• cos(A-B)=sinA sinB +cosA

cos B}

= cos x= R.H.S

HENCE.PROVED.....

Answer 2

Answer:

Cos A

Step-by-step explanation:

Cos (X - Y) = Cos X Cos Y + Sin X Sin Y

here X = (n+2)A. Y = (n+1) A

Hence, sin((n + 1)A] sin((n + 2)A] + cos((n + 1)A] cos((n + 2)A] is equal to Cos [ (n+2)A - (n+2) A]

= Cos A