Question

lim x tends to 0:cos2x-1÷cosx-1

Answer 1

$\lim_{x \to 0} \frac{ \cos2x- 1 }{ \cos x - 1 } \\ = \lim_{x \to 0} \frac{(2 { \cos }^{2} x - 1)- 1 }{ \cos x - 1 } \\ = \lim_{x \to 0} \frac{2 { \cos }^{2} x - 2}{ \cos x - 1 } \\ = \lim_{x \to 0} \frac{2( { \cos }^{2} x - 1)}{ \cos x - 1 } \\ = \lim_{x \to 0} \frac{2( \cos x + 1)( \cos x - 1)}{ \cos x - 1 } \\ = \lim_{x \to 0}2( \cos x + 1) \\ = 2( \cos(0) + 1) = 2(1 + 1) = 4$