Question

if ( cos theta + sin theta ) = root 2 theta, show that (sin theta - cos theta) = root 2 cos theta

Answer 1

Step-by-step explanation:

--> 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