1-cos-co-cos-1-cos-cos-cos-tan-2-cot-2-

Question Number 43810 by gyugfeet last updated on 15/Sep/18

\frac{1 - c o s θ + c o β - c o s (θ + β)}{1 + c o s θ - c o s β - c o s (θ + β)} = t a n \frac{θ}{2} . c o t \frac{β}{2}

Answered by tanmay.chaudhury50@gmail.com last updated on 15/Sep/18

= \frac{2 {s i n}^{2} \frac{θ}{2} + 2 s i n (\frac{θ}{2} + β) s i n (\frac{θ}{2})}{2 {c o s}^{2} (\frac{θ}{2}) - 2 c o s (\frac{θ}{2} + β) c o s (\frac{θ}{2})}

= t a n \frac{θ}{2} \times \frac{s i n \frac{θ}{2} + s i n (\frac{θ}{2} + β)}{c o s (\frac{θ}{2}) - c o s (\frac{θ}{2} + β)}

= t a n (\frac{θ}{2}) \times \frac{2 s i n (\frac{θ + β}{2}) c o s (\frac{β}{2})}{2 s i n (\frac{θ + β}{2}) s i n (\frac{β}{2})}

= t a n (\frac{θ}{2}) c o t (\frac{β}{2})