Question

0. If none of the angles x,y and (x + y) is an odd multiple of
then
2
tan (x + y) =
tan x + tany
1 tan x tany​

Answer 1

Answer:

(i) As x,y and x+y are not the odd multiple

2

π

∴cosx,cosy and cos(x+y) are non-zero.

Now tan(x+y)=

cos(x+y)

sin(x+y)

=

cosxcosy−sinxsiny

sinxcosy+cosxsiny

Dividing numerator and denominator by cosxcosy, we get

tan(x+y)=

cosxcosy

cosxcosy

−

cosxcosy

sinxsiny

cosxcosy

sinxcosy

+

cosxcosy

cosxsiny

=

1−tanxtany

tanx+tany

(ii) We have

tan(x+y)=

1−tanxtany

tanx+tany

Now replace y by −y, we get

tan[x−(−y)]=

1−tanxtan(−y)

tanx+tan(−y)

∴tan(x−y)=

1+tanxtany

tanx−tany