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Question
Evaluate `lim_(x -> 0) (cos ax - cos bx)/(cos cx - 1)`
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Solution
We have `lim_(x -> 0) (2sin ((a + b))/2 x sin ((a - b) x)/2)/(2 (sin^2 cx)/2)`
= `lim_(x -> 0) (2sin ((a + b)x)/2 * sin ((a - b)x)/2)/x^2 * x^2/(sin^2 (cx)/2)`
= `lim_(x -> 0) (sin ((a + b)x)/2)/(((a + b)x)/2 * 2/(a + b)) * (sin ((a - b)x)/2)/(((a - b)x)/2 * 2/(a - b)) * ((cx)^2/2 xx 4/c^2)/(sin^2 (cx)/2)`
= `(a + b)/2 xx (a - b)/2 xx 4/c^2`
= `(a^2 - b^2)/c^2`
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