Question

If cos theta + sin theta = √2, then cos theta - sin theta = ?​

Answer 1

--> cos θ + sin θ = √2 cos θ

--> sin θ = √2 cos θ - cos θ

=> sin θ = ( √2 - 1 ) cos θ

=> [ sin θ / ( √2 - 1 ) ] = cos θ

=> [ sin θ ( √2 + 1 ) / ( 2 - 1 ) ] = cos θ

0_0 --> We rationalized the denominator in the 2nd step ^_^

=> [ √2 sin θ + sin θ ] = cos θ

=> cos θ - sin θ = √2 sin θ

Answer 2

Answer:

your answer attached in the photo