Prove and compute the limit of this function.&nbsp;limx→0+sin(6x)sin(2x)&nbsp;Trying converting it into different functions like&nbsp;cos(π2−2x)&nbsp;or multiplying by the inverse function and so on, but it keep getting back to&nbsp;0/0.

Question

Prove and compute the limit of this function.&amp;nbsp;limx→0+sin(6x)sin(2x)&amp;nbsp;Trying converting it into different functions like&amp;nbsp;cos(π2−2x)&amp;nbsp;or multiplying by the inverse function and so on, but it keep getting back to&amp;nbsp;0/0.

Cheryl King · Accepted Answer

Hint:   sin⁡6xsin⁡2x=sin⁡6xsin⁡2x⋅sin⁡2x

peterpan7117i · Accepted Answer

You can do this with regular old trig identities. Note that:  sin⁡6x=6sin⁡xcos5x−20sin3xcos3x+6sin5xcos⁡x  sin⁡2x=2sin⁡xcos⁡x  For shorthand, let me write:    sin⁡(x)=S     cos⁡(x)=C   So your ratio is:   limx→0+sin⁡6xsin⁡2x=6SC5−20S3C3+6S5C2SC  =6SC5−20S2SC3+6S4SC2C  Finally, we have a form where the denominator wont

Vasquez · Accepted Answer

Hint sin⁡6xsin⁡2x=6xsin⁡6x6x2xsin⁡2x2x

Prove and compute the limit of this function. lim__(x->0)(sin(6x))/(sqrt(sin(2x)))

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