Mathematics: True or false: the equation sec^2 x - 1 = tan^2 x is an identity.

True or false: the equation sec^2 x - 1 = tan^2 x

Ответ:

ayeeitsenaly4175

31.12.2021

Use the trigonometric identities:
$\sec x= \frac{1}{\cos x} \\
\tan x= \frac{\sin x}{\cos x} \\
\sin^2 x+ \cos^2 x=1$

$\sec^2 x-1=\tan^2 x \\
(\frac{1}{\cos x})^2-1=(\frac{\sin x}{\cos x})^2 \\
\frac{1}{\cos^2 x}-1 = \frac{\sin^2 x }{\cos^2 x} \ \ \ |\times \cos^2 x \\
1-\cos^2 x=\sin^2 x \ \ \ |+\cos^2 x \\
\sin^2x+\cos^2x=1 \\ \boxed{\hbox{true}}$

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Ответ:

carlydays3331

17.11.2020

Mathematics

I would think the first 2 and the third one because two of the same numbers over each other are equal to 1

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True or false: the equation sec^2 x - 1 = tan^2 x is an identity.

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