(sinα/1+cosα)+1+cosα/sinα=2/sinα

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To solve this equation, we need to find a common denominator for the two fractions:

(sinα/(1+cosα)) + (1+cosα)/sinα = 2/sinα

Multiplying the first fraction by (1+cosα) and the second fraction by sinα, we get:

(sinα(1+cosα) + (1+cosα)sinα)/((1+cosα)sinα) = 2/sinα

Expanding and simplifying the numerator:

(sinα + sinαcosα + sinα + cosαsinα)/((1+cosα)sinα) = 2/sinα

(2sinα + 2sinαcosα)/((1+cosα)sinα) = 2/sinα

Now, we can cancel out the sinα terms:

2 + 2cosα = 2

2cosα = 0

cosα = 0

Therefore, the solution to the equation is α = π/2 + nπ, where n is an integer.