Question

If cos theta plus sin theta equals to under root two cos theta . Show that cos theta minus sin theta equals to under root two sin theta

Answer 1

=> cos ø + sin ø = √2 cos ø

=> sin ø = √2 cos ø - cos ø

=> sin ø = cos ø [ √2 - 1 ]

=> sin ø / √2 - 1 = cos ø

Rationalize the denominator ....

=> sin ø / √2-1 × √2+1 / √2+1 = cos ø

=> sin ø ( √2 + 1 ) / (√2) ^2 - (1) ^2 = cos ø

=> √2 sin ø + sin ø / 2 - 1 = cos ø

=> √2 sin ø + sin ø = cos ø

=> √2 sin ø = cos ø - sin ø

i.e., cos ø - sin ø = √2 sin ø

Hence proved ....

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