Find the sum : $\frac{1}{\cos0^\circ\cos1^\circ}+\frac{1}{\cos1^\circ \cos2^\circ} +\frac{1}{\cos2^\circ \cos3^\circ}+......+$
Solution 1:
HINT:
$$\frac{\sin(A-B)}{\cos A\cos B}=\frac{\sin A\cos B-\cos A\sin B}{\cos A\cos B}=\tan A-\tan B$$
If $A= (n+1)^\circ,B=n^\circ$
$$\frac{\sin 1^\circ}{\cos (n+1)^\circ\cos n^\circ}=\tan(n+1)^\circ-\tan n^\circ $$
Put $n=0,1,2,\cdots,87,88$ and add to find the series to be Telescopic