Question

pls help......No spam pls

​

Answer 1

Answer:

LHS

= 1/cot^2(cosec -1/1+cos ) - 1/sin^2 (cos -1 / 1+ cosec )

= 1/cosec^2 -1 (cosec -1 / 1+ cos ) +1/1-cos^2 (1-cos/1+cosec)

= 1/(cosec+1)(1+cos) + 1/(1+cos)(1+cosec)

= 2/(1+cos)(1+1/sin) = 2sin/(1+cos)(1+sin)

Answer 2

$\sf \huge \color{purple} \underline{\underline{Question }} :$

$\large \sf \color{Green} tan²\theta(\frac{Cosec\theta-1}{1+cos\theta})-Cosec²\theta(\frac{Cos\theta-1}{1-Cosec})$

$\sf \huge \color{purple} \underline{\underline{Solution }} :$

$\large \sf (\frac{1}{Cot²\theta})(\frac{Cosec\theta-1}{1+cos\theta})-\frac{1}{Sin²\theta}(\frac{Cos\theta-1}{1-Cosec}) \\ \\ \large \sf (\frac{1}{Cosec²\theta -1²\theta})(\frac{Cosec\theta-1}{1+cos\theta})-\frac{1}{1²-cos²\theta}(\frac{Cos\theta-1}{1-Cosec}) \\ \\ \large \sf (\frac{1}{Cosec\theta -1})(\frac{Cosec\theta-1}{1+cos\theta})-\frac{1}{(1-cos\theta)(1+cos\theta}(\frac{Cos\theta-1}{1-Cosec})$