tolong dong bantuin caranya bagaimana
Answer (1)
[tex] \lim \limits_{x \to \: 0} \frac{csc \: 2x - cot \: 2x}{tan \: 3x} [/tex][tex] = \lim \limits_{x \to \: 0} \frac{ \frac{1}{sin \: 2x} - \frac{1}{tan \: 2x} }{tan \: 3x} [/tex][tex] = \lim \limits_{x \to \: 0} \frac{ \frac{1}{sin \: 2x} - \frac{cos \: 2x}{sin \: 2x} }{tan \: 3x} [/tex][tex] = \lim \limits_{x \to \: 0} \frac{1 - cos \: 2x }{sin \: 2x \: tan \: 3x} [/tex][tex] = \lim \limits_{x \to \: 0} \frac{1 - (1 - 2{sin}^{2}) }{sin \: 2x \: tan \: 3x} [/tex][tex] = \lim \limits_{x \to \: 0} \frac{2{sin}^{2} x}{sin \: 2x \: tan \: 3x} [/tex][tex] = 2 \lim \limits_{x \to \: 0} \frac{sin \: x}{sin \: 2x} \lim \limits_{x \to \: 0}\frac{sin \: x}{tan \: 3x} [/tex][tex] = 2 \frac{1}{2} \frac{1}{3} [/tex][tex] = \boxed{\frac{1}{3}}[/tex]
