solve question no. 4
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Heya !!
( CosX + SinX) = ✓2 Cos X ------(1)
=> ( CosX + SinX)² = 2Cos²X
=> Cos²X + Sin²X + 2SinX CosX = 2Cos²X
=> Cos²X - Sin²X = 2 SinX CosX
=> ( Cos X + SinX ) ( Cos X - SinX ) = 2SinXCosX.
=> ( ✓2 Cos X ) ( Cos X - SinX ) = 2SinX CosX [ Using (1) ]
=> ( Cos X - Sin X ) = 2SinX Cos X/ ✓2Cos X
=> ( Cos X - Sin X ) = ✓2 Sin X
Hence,
( Cos X - Sin X ) = ✓2 Sin X.
( CosX + SinX) = ✓2 Cos X ------(1)
=> ( CosX + SinX)² = 2Cos²X
=> Cos²X + Sin²X + 2SinX CosX = 2Cos²X
=> Cos²X - Sin²X = 2 SinX CosX
=> ( Cos X + SinX ) ( Cos X - SinX ) = 2SinXCosX.
=> ( ✓2 Cos X ) ( Cos X - SinX ) = 2SinX CosX [ Using (1) ]
=> ( Cos X - Sin X ) = 2SinX Cos X/ ✓2Cos X
=> ( Cos X - Sin X ) = ✓2 Sin X
Hence,
( Cos X - Sin X ) = ✓2 Sin X.
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