6. If cos 0 -sin 0 = V2 sin 0, prove that cos 0 + sin 0 = V2cos​

2 thoughts on “6. If cos 0 -sin 0 = V2 sin 0, prove that cos 0 + sin 0 = V2cos​”

1. Answer:

   Correct Question

   If cos∅ + sin∅ = √2 cos∅, then prove that cos∅ – sin∅ = √2 sin∅.

   Proof

   → cos∅ + sin∅ = √2 cos∅

   → sin∅ = √2 cos∅ – cos∅

   → sin∅ = cos∅(√2 – 1)

   → sin∅/(√2 – 1) = cos∅

   On rationalizing we get,

   → sin∅/(√2 – 1) × (√2 + 1)/(√2 + 1) = cos∅

   → sin∅(√2 + 1)/(2 – 1) = cos∅

   → √2 sin∅ + sin∅ = cos∅

   → √2 sin∅ = cos∅ – sin∅

   Or cos∅ – sin∅ = √2 sin∅

   Hence Proved

   HOPE THIS HELPS YOU !

   Reply

2. Answer:

   please refer to the image uploaded

   Reply