Answer:
Step-by-step explanation:
[tex]\frac{cot \theta}{cosec \theta + 1} = \frac{cosec\theta -1} {cot \theta}[/tex]
[tex]L H S[/tex]
[tex]\frac{cot \theta }{cosec \theta + 1 } \times \frac{cosec \theta - 1}{cosec \theta -1}[/tex] [tex][ \ multiplying \ and \ dividng \ by \ (cosec \theta - 1) \ ][/tex]
[tex]= \frac{cot \theta \times (cosec \theta - 1)}{(cosec ^2\theta -1)}[/tex] [tex][ \ (a -b)(a+b) = a^2 - b^2 \ ][/tex]
[tex]= \frac{cot \theta \times (cosec \theta - 1)}{cot^2 \theta}\\ \\[/tex] [tex][ \ cosec^2\theta - 1 = cot^2 \theta \ ][/tex]
[tex]= \frac{cosec \theta - 1 }{cot \theta} \\\\= RHS[/tex]
