cosa+sina=root2cosa then provethat cosa-sina=root2sina
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cos∅ + sin∅ = √2cos∅
take square both sides ,
cos²∅ +sin²∅ +2sin∅.cos∅ = 2cos²∅
cos²∅ - sin²∅ = 2sin∅.cos∅
( cos∅ - sin∅)( cos∅+sin∅) = 2sin∅.cos∅
(cos∅-sin∅) × √2cos∅ = 2sin∅.cos∅
cos∅ - sin∅ = √2sin∅
hence proved
take square both sides ,
cos²∅ +sin²∅ +2sin∅.cos∅ = 2cos²∅
cos²∅ - sin²∅ = 2sin∅.cos∅
( cos∅ - sin∅)( cos∅+sin∅) = 2sin∅.cos∅
(cos∅-sin∅) × √2cos∅ = 2sin∅.cos∅
cos∅ - sin∅ = √2sin∅
hence proved
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