Question

General solutions of tan x + tan 2x + tan 3x =0

Answer 1

Step-by-step explanation:

LHS=

cosx

sinx

+

cos 2 x

sin 2 x

+

cos 3 x

sin 3 x

=

cosxcos2x

sinxcos2x+cosxsin2x

+

cos 3 x

sin 3 x

=

cosxcos2x

sin3x

+

cos 3 x

sin 3 x

sin3x=

0

or

cos3x+

cosxcos2x=

0

sin3x=

0

or

2cos3x+

2cosxcos2x=

0

sin3x=

0

or

2cos3x+

cos3x+

cosx=

0

sin3x=

0

or

3cos3x+

cosx=

0

sin3x=

0

or

3(4cos

3

x−

3cosx)+

cosx=

0

x=

nπ

or

x=

nπ±

3

π