Evaluate the following limits: `lim_(xrarr0)(cos ax-cos bx)/(cos cx-1)

1.	Evaluate the following limits: `lim_(xrarr0)(cos ax-cos bx)/(cos cx-1)`
Answer» Correct Answer - `((a^(2)-b^(2)))/(c^(2))` Given limit `=lim_(xto0)(-2sin((a+b)/(2))x.sin((a-b)/(2))x)/(-2sin^(2)((cx)/(2)))` `((sin((a+b)/(2))x)/(((a+b)/(2)))xx((a+b)/(2))x.(sin((a-b)/(2))x)/(((a-b)/(2))x)xx((a-b)/(2))x)/({(sin((cx)/(2)))/(((cx)/(2)))}^(2))` `={((a+b)/(2))((a-b)/(2))xx(4)/(c^(2))}.lim_(xto0)(sin((a+b)/(2))x)/(((a+b)/(2))).lim_(xto0)(sin((a-b)/(2))x)/(((a-b)/(2))x)` `={((a^(2)-b^(2)))/(x^(2))xx1xx1}=((a^(2)-b^(2)))/(c^(2)).`

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