Kronig penney model in reciprocal space

goldfalcon
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at page 174 there is a result for kronig penney model in reciprocal space whic equals 1/a when i tried to it i am obtaining 1+1/a with mathematice so what is wrong do you know how to evaulate in more detail??how to obtain 1/a?? thx
 
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that problem is done that post may be deleted thx..
 
Hi I had this doubt too.. can you tell me how its done? And the final step too.. what trigonometric identities have they used?
 

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