Question

$\underset{x\to 0}{lim}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to

• A. 2
• B. 1/2
• C. 4
• D. 3

Answer 1

Answer: (A)

2

${lim}_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}\Rightarrow \frac{(1-1+2\sin {}^{2}x)(3+\cos x)}{x\times 4x}\times \left(\frac{4x}{\tan 4x}\right)\Rightarrow \frac{2\sin {}^{2}x}{4x^2}\times (3+\cos x)\times 1\Rightarrow \frac{1}{2}{\left(\frac{\sin x}{x}\right)}^2\times (3+\cos x)\times 1\Rightarrow \frac{1}{2}\times 4\times 1=2$