Question

Solution for (1+cotA-cosecA)(1+tanA-secA)=2. Prove

Answer 1

here's your answer .
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Answer 2

$(1 + cota - coseca)(1 + tana + cota) \\ \\ = ( \frac{sina + cosa - 1}{sina} )( \frac{cosa + sina + 1}{cosa} ) \\ \\ = \frac{( {sina + cosa)}^{2} - 1 }{sinacosa} \\ \\ = \frac{2sinacosa}{sinacosa} \\ \\ = 2$