Question

tan2theta - cot2theta = 0 for 0 < theta < 180degrees

Answer 1

tan2x - cot2x = 0
tan2x - 1/tan2x = 0
multiply by tan2x to both sides, gives
tan^2 2x - 1 = 0
(tan2x+1)(tan2x-1) = 0
for zeroes, take : tan2x+1=0 or tan2x-1=0
for tan2x+1=0,
case I :
tan2x+1=0
tan2x=-1
tan2x=tan3pi/4
tan2x=tan(k*pi+3pi/4)
2x = k*pi + 3pi/4
x = k*pi/2 + 3pi/8
case II :
tan2x=-1
tan2x=tan7pi/4
but, u neednt solve it (because just for interval 0 < x < 180degrees)
for tan2x-1=0
case I :
tan2x-1=0
tan2x = 1
tan2x = tan pi/4
tan2x = tan (k*pi + pi/4)
2x = k*pi + pi/4
x = k*pi/2 + pi/8
case II :
tan2x = 1
tan2x = tan 5pi/4
but, needn't solve it (because just for interval 0 < x < 180degrees)

sorry, i was change theta be "x" :)