Question

Identities- Ugh!
1÷cscθ−cotθ=1+cosθ÷sinθ

Answer 1

r u missing any brackets?

Answer 2

It should be:\[\frac{ 1 }{ \csc \theta - \cot \theta }=\frac{ 1+\cos \theta }{ \sin \theta }\]Let's begin at the left hand side:\[\frac{ 1 }{ \csc \theta - \cot \theta }=\frac{ 1 }{ \frac{ 1 }{ \sin \theta }-\frac{ \cos \theta }{ \sin \theta } }=\frac{ 1 }{ \frac{ 1-\cos \theta }{ \sin \theta } }=\frac{ \sin \theta }{ 1- \cos \theta }\]This looks much better, although it is not quite the right hand side yet...

Hint: multiply numerator and denominator of the last fraction with (1+cosθ)/(1+cosθ):\[\frac{ \sin θ }{ 1-\cos θ } \cdot \frac{ 1+\cos θ }{ 1+\cos θ }= ...\]After just a few small steps, you'll have got to the right hand side of the identity!