Q:

Solving this trigonometric summation: $\sum_{i=1}^{88}{\frac{1}{\cos i°\cdot cos(i+1)°}}$

How would we solve this summation? 
$$\sum_{i=1}^{88}{\frac{1}{\cos i°\cdot \cos(i+1)°}}$$
I can't seem to make a start anywhere...

A:

$\sum_{i=1}^{88}{\frac{1}{\cos i° \times \cos(i+1)°}} = \frac{1}{\sin(1°)}\sum_{i=1}^{88}{\frac{\sin((i+1) - (i))°}{\cos i° \times \cos(i+1)°}} = \frac{1}{\sin(1°)}\sum_{i=1}^{88}{\frac{\sin(i+1)°\cos(i°) - \cos(i+1)°\sin(i°)}{\cos i° \times \cos(i+1)°}} = \frac{1}{\sin(1°)}\sum_{i=1}^{88}{\tan(i+1)° - \tan(i)°} = \frac{\tan(89°) - \tan(1°)}{\sin(1°)}$

