Odd Geometric progression

Geometry Level 4

A geometric progression \( a_n \) satisfies:

\[ a_1 = \sin x, \ a_2 = \cos x, \ a_3 = \tan x, \ \ldots \]

for a certain value of \(x\).

For what value of \(n\) do we have \( a_n = 1 + \cos x \)?

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