Limiting sum trig (1 Viewer)

[enigma_1]

Can you help me with this?

Find in terms of t=tan1/2x, the limiting sum of this series as it converges:

1-sinx + sin^2x - ....

 

[cineti970128]

The first term is 1 and common ratio is -2t/(1+t^2)
So use the GP infinite formula a/(1-r)
Note that |sinx|<= 1 so you can use day formula.