How Do You Solve lim(x->0) tan(3x)/sin(8x) Using Trigonometric Limits?

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To solve the limit lim(x->0) tan(3x)/sin(8x), the approach involves using the limit property lim(x->0) sin(x)/x = 1. The expression is transformed to {1/cos(3x)} * {sin(3x)/sin(8x)}, where 1/cos(3x) approaches 1 as x approaches 0. The challenge lies in simplifying the term {sin(3x)/sin(8x)}, which can be resolved by multiplying and dividing by 24x to facilitate the limit calculation. Ultimately, applying these techniques leads to the correct evaluation of the limit.
donjt81
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I'm trying to solve this problem

lim(x->0) tan(3x)/sin(8x)

using the formula lim(x->0) sinx/x = 1

so i did the following

tan(3x)/sin(8x)
{sin(3x)/cos(3x)}/sin8x
{1/cos(3x)} * {sin(3x)/sin(8x)}

now I know the term {1/cos(3x)} becomes 1 when you apply the limit but I have no idea how to solve the second term which is {sin(3x)/sin(8x)}...

can anyone please help

Thanks
 
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Hint: Multiply and divide by 24x. ;)
 
I'd rather expand the fraction with the factor 24x.
 
got it... thanks guys
 

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