number of solution of tanx + sec x = 2 cosxx belongto [0,2pi] are ??? answer is 2 but EXPLAIN why and how??

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Sum of series 2[n/2] ! [n/2]!/ n! [2Co-2C2+3C2....+[-1]^n[n+1]2Cn] where n is an even positive integer. Kindly provide solution of this question and how to generalise this. How do we know that which expansion will give this?

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