- #1
SonyDvDPro
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Find [tex]\mathop {\lim }\limits_{x \to 0} \frac{{\tan (nx) - n\tan (x)}}
{{n\sin (x) - \sin (nx)}} [/tex]
{{n\sin (x) - \sin (nx)}} [/tex]
dynamicsolo said:exploit the heck out of
lim u->0 (sin u)/u = 1 .
The purpose of limiting the expression of tangent and sine is to restrict the values of these trigonometric functions to a specific range, typically between -1 and 1, in order to simplify calculations and make them more manageable.
The expression of tangent and sine is limited by using certain rules and identities, such as the Pythagorean identity and the unit circle, to transform the original expression into a simpler form that falls within the desired range.
It is important to limit the expression of tangent and sine because it allows for more accurate and precise calculations in various fields such as mathematics, physics, and engineering. It also helps to avoid errors and confusion when working with these functions.
Some common examples of limiting the expression of tangent and sine include using trigonometric identities to simplify expressions, applying the unit circle to find equivalent values, and using inverse trigonometric functions to find restricted values.
Yes, the expression of tangent and sine can be limited to any desired range. It is common to limit them to values between -1 and 1, but they can also be limited to other ranges depending on the specific needs of a problem or calculation.