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Heya User,
---> sin θ + cos θ = 1
=> [ sin θ + cos θ ]² = 1
=> [ sin² θ + cos² θ ] + 2 (sin θ)(cos θ) = 1
=> 1 + 2 (sin θ)(cos θ) = 1
=> 2 (sin θ)(cos θ) = 0 ;
Now, [ sin² θ + cos² θ ] = 1
===> [ sin² θ - 2 (sin θ)(cos θ) + cos² θ ] = 1 + 0
===> [ sin θ - cos θ ]² = 1
===> sin θ - cos θ = ± 1 ^_^ Proved..
---> sin θ + cos θ = 1
=> [ sin θ + cos θ ]² = 1
=> [ sin² θ + cos² θ ] + 2 (sin θ)(cos θ) = 1
=> 1 + 2 (sin θ)(cos θ) = 1
=> 2 (sin θ)(cos θ) = 0 ;
Now, [ sin² θ + cos² θ ] = 1
===> [ sin² θ - 2 (sin θ)(cos θ) + cos² θ ] = 1 + 0
===> [ sin θ - cos θ ]² = 1
===> sin θ - cos θ = ± 1 ^_^ Proved..
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