Question

Write the value of ${lim}_{x\to \frac{\pi }{2}}\frac{2x-\pi }{cosx}.$

Answer 1

${lim}_{x\to \frac{\pi }{2}}\frac{2x-\pi }{\cos x}.={lim}_{x\to 0}\frac{2(\frac{\pi }{2}-x)-\pi }{\cos (\frac{\pi }{2}-x)}={lim}_{x\to 0}\frac{-2x}{\sin x}={lim}_{x\to \frac{x}{2}}\frac{2x-\pi }{\cos x}=-2$