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Sagot :
The expression of [tex] \mathbf{sec( \theta)}[/tex] in terms of [tex]tan( \theta)[/tex] in Quadrant IV is presented as follows;
[tex] sec( \theta) = \sqrt{{tan( \theta)}^{2} + 1} [/tex]
Which trigonometric identity can be used to express the required function?
The given trigonometric functions are;
[tex]sec( \theta)[/tex]
[tex]tan( \theta)[/tex]
[tex] {sec( \theta)}^{2} = {tan( \theta)}^{2} + 1[/tex]
In Quadrant IV, the tangent of an angle is -ve, while the secant is +ve
However, the square of -ve is positive;
- (-ve)² = +ve
Therefore;
[tex] \left({tan( \theta)}^{2} + 1 \right) \: is \: positive[/tex]
Which gives;
- [tex] sec( \theta) = \sqrt{{tan( \theta)}^{2} + 1} [/tex]
Learn more about regular trigonometric identities here:
https://brainly.com/question/12335464
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