Mathematics: How do you prove: csc^[email protected]^[email protected] = csc^[email protected] -1

How do you prove: csc^[email protected]^[email

Ответ:

kennedyrc12

31.12.2021

$cscx=\frac{1}{sinx};\ sin^2x+cos^2x=1\to cos^2x=1-sin^2x\\----------------------------\\\\csc^2xcos^2x=csc^2x-1\\\\L=csc^2xcos^2x=\frac{1}{sin^2x}\cdot cos^2x=\frac{cos^2x}{sin^2x}\\\\R=csc^2x-1=\frac{1}{sin^2x}-1=\frac{1}{sin^2x}-\frac{sin^2}{sin^2x}=\frac{1-sin^2x}{sin^2x}=\frac{cos^2x}{sin^2x}\\\\\boxed{L=R}$

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Ответ:

charityclark3935

31.12.2021

Mathematics

$LHS\\ \\ ={ cosec }^{ 2 }\theta { cos }^{ 2 }\theta \\ \\ ={ cosec }^{ 2 }\theta \left( 1-{ sin }^{ 2 }\theta \right)$

$\\ \\ ={ cosec }^{ 2 }\theta -{ cosec }^{ 2 }\theta { sin }^{ 2 }\theta \\ \\ ={ cosec }^{ 2 }\theta -\frac { 1 }{ { sin }^{ 2 }\theta } \cdot { sin }^{ 2 }\theta$

$\\ \\ ={ cosec }^{ 2 }\theta -1\\ \\ =RHS$

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Ответ:

ugum

16.10.2022

Mathematics

Khsgkzhsrnzmd6kfk. lgccgokcfi

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How do you prove:
csc^[email protected]^[email protected] = csc^[email protected] -1

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