Question

sin (x+y) - 2sin x + sin(x-y)
cos (x + y) - 2cos x + cos (x-y)
= tan x​ prove this.... PLS HELP

Answer 1

Step-by-step explanation:

sin (x+y)=sinxcosy+sinycosx

sin (x-y)=sinxcosy-sinycosx

cos (x+y)=cosxcosy-sinxsiny

cos (x-y)=cosxcosy+sinxsiny

.

.

so,

[sin (x+y) + sin (x-y)] / [cos (x+y) + cos (x-y)]

=[sinxcosy+sinycosx + sinxcosy - sinycosx] /[cosxcosy-sinxsiny +cosxcosy+sinxsiny]

=(2 sinxcosy ) / (2 cosxcosy )

=sinx/cosx

=tanx