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

Sagot :

naǫ
Use the trigonometric identities:
[tex]\sec x= \frac{1}{\cos x} \\ \tan x= \frac{\sin x}{\cos x} \\ \sin^2 x+ \cos^2 x=1[/tex]

[tex]\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}}[/tex]

Answer:

True

Step-by-step explanation:

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