Question

find the general solutions of : tan x+ cot 2x = 0

Answer 1

fisrt change in terms of sin and cos and then simplify fuirther

Answer 2

tan x+ cot 2x = 0
sinx/cosx + cos2x/sin2x =0
sinxsin2x+cosxcos2x= 0
cos(2x-x)=0
or cosx =0....and further..

Answer 3

Note that there is a trig identity for cot 2x. You might want to look up "trig identities" and look for it. Alternatively, you could re-write cot 2x as cos2x/sin2x, as "matricked" has done.

Answer 4

even i got cos x = 0 but the general solution given is n (pi)- pi/2 .. which i am not getting @matricked @mathmale

Answer 5

if cos x =0
then x= odd multiples of (pi/2)

Answer 6

x= (2n-1)(pi/2) = n(pi) - (pi/2)

Answer 7

A solution involving n, such as this one, stems from the periodicity of the sine and cosine functions. The cosine function repeats itself every 2Pi radians. cos x = 0 at x = Pi/2; this is true again at 2Pi + Pi/2, at 4Pi + Pi/2, and so on; that's where the n2Pi comes from.

Note that cos x is 0 also at x =3Pi/2; the same pattern happens here also.