What is the is the solution for this:
Establish :
tan theta + cot theta
--------------------- = csc² theta
tan theta
tan theta + cot theta =
tan theta + 1 / tan theta =
tan theta * tan theta / tan theta + 1 / tan theta =
tan ^ 2 theta / tan theta + 1 / tan theta =
( tan ^ 2 theta + 1 ) / tan theta =
( sin ^ 2 theta / cos ^ 2 theta + cos ^ 2 theta ) / tan theta =
[ ( sin ^ 2 theta + cos ^ 2 theta ) / cos ^ 2 theta ] / tan theta =
( 1 / cos ^ 2 theta ) / tan theta =
1 / ( cos ^ 2 theta * tan theta ) =
1 / ( cos ^ 2 theta * sin theta / cos theta ) =
( 1 / cos theta * sin thheta )
1 / cos theta * 1 / sin theta =
sec theta * csc theta
( tan theta + cot theta ) / tan theta = csc theta
( sec theta * csc theta ) / tan theta = csc theta Divide both sides by csc theta
sec theta / tan theta = 1
1 / cos theta / ( sin theta / cos theta ) = 1
1 * cos theta / ( sin theta * cos theta ) = 1
1 / sin theta = 1
csc theta = 1
The solution is :
theta = pi / 2 + OR - 2 n * pi
where n is integer number