Question

prove that 1+cos theta /1-cos theta -1-cos theta/1+cos theta =4 cot theta×cosec theta​

Answer 1

Answer:

LHS=1+cos theta /1-cos theta -1-cos theta/1+cos theta

RHS=4 cot theta×cosec theta​

$LHS=\frac{1+cos theta }{1-cos theta} -\frac{1-cos theta}{1+cos theta}\\(divide both numerator and denominator with sintheta)\\=\frac{cosectheta+cottheta}{cosectheta-cottheta} -\frac{cosectheta-cottheta}{cosectheta+cottheta}\\=\frac{(cosectheta+cottheta)^2+(cosectheta-cottheta)^2}{(cosectheta-cottheta)(cosectheta-cottheta)} \\=\frac{4(cosecthetacottheta}{cosec^2theta-cot^2theta} \\=4cosecthetacottheta/1\\=4cosectheta.cottheta=RHS$