Question

Does anyone know how to do this

csc x ( sin x + cos x) = 1 + cot x ​

Answer 1

9514 1404 393

Explanation:

Use the identities ...

  csc(x) = 1/sin(x)

  cot(x) = cos(x)/sin(x)

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  $\csc(x)(\sin(x)+\cos(x))=1+\cot(x)\\\\\dfrac{1}{\sin(x)}(\sin(x)+\cos(x))=1+\cot(x)\\\\\dfrac{\sin(x)}{\sin(x)}+\dfrac{\cos(x)}{\sin(x)}=1+\cot(x)\\\\1+\cot(x)=1+\cot(x)$