Question

SinQ/cosecQ+cotQ=1-cos Q
Please answer

Answer 1

Step-by-step explanation:

Aloha !

sin theta/cosec theta +cot theta=1-cos theta

sin ∅ /1-cos∅=cosec∅+ cot∅

sin∅(1+cos∅)/1-cos∅×1+cos∅

sin∅(1+cos∅)/1-cos²∅

sin∅(1+cos∅)/sin²∅

1/sin∅+cos∅/sin∅

=cosec∅+cot∅

Thank you

@ Twilight Astro ✌️☺️♥️

Answer 2

Answer:

$\huge\underline{ \underline{ \red{your \: \: answer}}}$

Step-by-step explanation:

$\sf\red{ \frac{sin \alpha }{cosec \alpha + cot \alpha } = 1 - cot \alpha } \\ \\ \sf\pink{ = >cosec \alpha + cot \alpha = \frac{sin \alpha }{1 - cot \alpha } } \\ \\ \sf\blue{R.H.S = \frac{sin \alpha }{1 - cos \alpha } } \\ \\ \sf\orange{ multypling \: \frac{numeratore}{denominator} \: by \: (1 + cos \alpha )} \\ \\ \sf\purple{ = > \frac{sin \alpha (1 + cos \alpha )}{(1 - cos \alpha )(1 + cos \alpha )} } \\ \\ \sf\green{ = > \frac{sin \alpha (1 - cos \alpha )}{ {1}^{2} - {cos}^{2} \alpha } } \\ \\ \sf\red{we \: know \: that \: {sin}^{2} \alpha + {cos}^{2} \alpha = 1 } \\ \\ \sf\pink{ = > {sin}^{2} \alpha = 1 - {cos}^{2} \alpha } \\ \\ \sf\green{now \: \: \frac{sin \alpha(1 + cos \alpha ) }{ {sin}^{2} \alpha } } \\ \\ \sf\blue{ = > \frac{1 + cos \alpha }{sin \alpha } } \\ \\ \sf\orange{ = > \frac{1}{sin \alpha } + \frac{cos \alpha }{sin \alpha } } \\ \\ \sf\red{ = > cosec \alpha + cot \alpha(L.H.S) } \\ \\ \sf\blue{R.H.S=L.H.S} \\ \sf\pink{ \underline{ \underline{proved} }} \\ \\ \\ \\ \large\boxed{ \fcolorbox{green}{yellow}{hope \: it \: help \: you}}$