The two equivalent forms of [tex]sec^2x[/tex] are [tex]\frac{1}{cos^2x}[/tex] and [tex]1+tan^2x[/tex]
Equivalent forms forms of trigonometric expressions
The given trigonometric expression is:
[tex]sec^2x[/tex]
Note that:
[tex]sec(x)=\frac{1}{cos(x)}[/tex]
Substitute this equivalence to the given expression
[tex]sec^2(x)=\frac{1}{cos^2(x)}[/tex]
Also from [tex]cos^2(x)+sin^2(x)=1[/tex]
Divide through by [tex]cos^2x[/tex]
[tex]\frac{cos^2x}{cos^2x} +\frac{sin^2x}{cos^2x}=\frac{1}{sin^2x}[/tex]
Simplifying the resulting expression:
[tex]1+tan^2x=sec^2x\\\\sec^2x=1+tan^2x[/tex]
Therefore, the two equivalent forms of [tex]sec^2x[/tex] are [tex]\frac{1}{cos^2x}[/tex] and [tex]1+tan^2x[/tex]
Learn more on equivalent forms of trigonometric expressions here:
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