Prove that siny/1+cosy +1+cosy/siny=2cosecy

    for the left-hand side:     we can try for a common denominator of  multiply the numerator and denominator of  by      multiply the numerator and denominator of  by      combining    expanding:     inserting:     addition order does not matter; i move sin²y and cos²y together so that i can use the pythagorean identity    pythagorean identity says that      so    factor out a 2 from the numerator    the  cancel and we are left with    by definition,     

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