Question

If cosecθ- sinθ= l and secθ - cosθ=m, prove that l²m² (l² m² 3) = 1

Answer 1

cosecФ-sinФ=L 1-sin²Ф/sinФ=L thus cotФcosФ=L secФ-cosФ=m 1-cos²Ф/cosФ=m thus tanФcosФ=m l²m²(l²+m²+3)=(cotФcosФtanФcosФ)²(cot²Фcos²Ф +tan²Фcos²Ф +3) =(cos²Ф)²(cos²Ф(cot²Ф+tan²Ф)+3) =1