Mathematics: Verify the identity. (cot x)/1+csc x)=(csc x-1)/(cot x) need showing work will a lot

Verify the identity. (cot x)/1+csc x)=(csc x-1)/(cot

Ответ:

lflwersl

18.01.2022

$\dfrac{\cot x}{1+\csc x}=\dfrac{\csc x-1}{\cot x}\\
\cot^2 x=(1+\csc x)(\csc x-1)\\
\cot^2 x=-(1+\csc x)(1-\csc x)\\
\cot^2 x=-(1-\csc^2 x)\\
\cot^2 x=-1+\csc^2 x\\
\left(\dfrac{\cos x}{\sin x}\right)^2=-1+\left(\dfrac{1}{\sin x}\right)^2\\
\dfrac{\cos^2 x}{\sin ^2x}=-1+\dfrac{1}{\sin^2 x}\\
\cos^2 x=-\sin^2x +1\\
\boxed{\sin^2 x+\cos ^2 x=1}$

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Ответ:

ladybugperez05

11.06.2020

Mathematics

what is a dummy.

Step-by-step explanation:

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Verify the identity.

(cot x)/1+csc x)=(csc x-1)/(cot x)

need showing work will a lot

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