Question

sin theta in the term cot theta

Answer 1

We know that,

cosec²∅ - cot²∅ = 1

=> cosec²∅ = 1 + cot²∅

We also know that,

cosec∅ = 1/sin∅

Now in cosec²∅ = 1 + cot²∅

Putting cosec²∅ as 1/sin²∅ we get,

1/sin²∅ = 1 + cot²∅

=> 1 = (sin²∅)(1 + cot²∅)

[By cross multiplication]

=> (sin²∅)(1 + cot²∅) = 1

=> sin²∅ = 1/(1 + cot²∅)

=>
$\sin( \alpha ) = \sqrt{ \frac{1}{1 + \cot {}^{2} ( { \alpha }^{} ) } } \\ \\ = > \sin( \alpha ) = \frac{1}{ \sqrt{1 + { \cot {}^{2} ( \alpha ) }^{} } }$

Here, alpha = ∅ (As I was not Able to find the symbol :/)

Your answer

sin∅ = 1/√(1 + cot²∅)

Hope it helps dear friend ☺️