[tex]\frac{cosx}{1+sinx}[/tex] is equivalent expression to [tex]\frac{1+sinx}{cosx}[/tex].
An expression in math is a statement involving at least two different numbers (known or unknown) and at least one operation.
Operations may include addition, subtraction, multiplication, division, exponents, and roots. The most important thing that defines an expression is what it doesn't have. Math expressions do not contain an equals sign (or a less than, greater than, or similar relation).
Given expression
[tex]\frac{cosx}{1+sinx}[/tex]
Rationalize the expression with 1 + sinx
= [tex]\frac{cosx}{1-sinx} \times \frac{1+sinx}{1+sinx}[/tex]
= [tex]\frac{cosx(1+sinx)}{(1-sinx)(1+sinx)}[/tex]
= [tex]\frac{cosx(1+sinx)}{1^{2}-(sinx)^{2} }[/tex]
= [tex]\frac{cosx(1+sinx)}{cos^{2}x }[/tex]
Cancel out cosx
= [tex]\frac{1+sinx}{cosx}[/tex]
[tex]\frac{cosx}{1+sinx}[/tex] is equivalent expression to [tex]\frac{1+sinx}{cosx}[/tex].
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