Limit h tends to zero $\lim_{h\rightarrow 0}\frac{1 – cosh}{hsinh}$

Limit h tends to zero $\lim_{h\rightarrow 0}\frac{1 – cosh}{hsinh}$

(ii) $\lim_{h\rightarrow 0}\frac{1 – cosh}{hsinh}$

= $\lim_{h\rightarrow 0}\frac{\cos^2\frac{h}{2} + sin^2\frac{h}{2} – cos^2\frac{h}{2} + sin^2\frac{h}{2}}{h(2sin\frac{h}{2}\cos \frac{h}{2})}$

= $\lim_{h\rightarrow 0}\frac{2sin^2\frac{h}{2}}{2hsin\frac{h}{2}\cos \frac{h}{2}}$

= $\lim_{h\rightarrow 0}\frac{\sin \frac{h}{2}}{h\cos \frac{h}{2}}$
= $\lim_{h\rightarrow 0}\frac{\sin \frac{h}{2}}{\frac{h}{2}} \times \frac{1}{\cos \frac{h}{2}} $

= $\lim_{h\rightarrow 0}\frac{\sin \frac{h}{2}}{\frac{h}{2}} \times \lim_{h\rightarrow 0}\frac{1}{\cos \frac{h}{2}}$

= 1.1

= 1