Verify the identities please.

Question

1.) TAN(X+π)-TAN(π-X)= 2 TAN X

2.) SIN(X+Y)+SIN(X-Y)= 2 SIN X COS Y

Answer 1

1. by the CAST rule
tan(π+Ø) = tanØ
tan(π-Ø) = -tanØ

LS = tan(x+π) - tan(π-x)
= tanx - (-tanx)
= 2tanx
= RS

2. again one of the standard identities used on the LS

LS = sinxcosy + cosxsiny + sinxcosy - cosxsiny
= 2sinxcosy
= RS
btw, 2sinxcosy = sin (2x) which would be a simplification of the RS

Answer 2

AWESOME! SUPERB! I had it right when you provided support. THANKS!