An intercepting line in geometry, especially one that intersects a circle at two points. In Trigonometry, A ratio of both the hypotenuse to an edge adjacent to a given angle in a rectangle. It definite line from the edge of the circle via one of the arc's ends to the tangential from another.
Following are the calculation to the given question:
Given:
[tex]\bold{\frac{\sin(2x)}{sinx}- \frac{cos(2x)}{cos x}}[/tex]
Using formula:
[tex]\bold{\sin 2x=2\sin x \cos x}\\\\\bold{\cos 2x=\cos^2 x - \sin^2 x}\\\\[/tex]
Apply the value in the given question:
[tex]\to \bold{\frac{\sin(2x)}{sinx}- \frac{cos(2x)}{cos x}}[/tex]
[tex]\to \bold{\frac{2 \sin x \cos x }{sinx}- \frac{(\cos^2 x -\sin^2 x) }{cos x}}\\\\\to \bold{2 \cos x - \frac{(\cos^2 x -\sin^2 x) }{cos x}}\\\\\to \bold{\frac{2 \cos^2 x - (\cos^2 x -\sin^2 x )}{cos x}}\\\\ \to \bold{\frac{2 \cos^2 x - \cos^2 x +\sin^2 x }{cos x}}\\\\ \to \bold{\frac{ \cos^2 x +\sin^2 x }{cos x}}\\\\ \to \bold{\frac{ 1 }{cos x}}\\\\ \to \bold{\sec x}\\\\[/tex]
So, the final answer is "sec x"
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