Question

√2cos (45+x)=cos x-sinx​

Answer 1

Solution :-

Q : √2cos (45 + x) = cosx - sinx

=> √2 sin (90 - 45 - x) = sin (90 - x) - sinx

=> √2 sin45° - sinx = sin90° - sinx - sinx

=> √2 × 1/√2 - sinx = 1 - sinx - sinx

=> 1 - 1 = - 2sinx + sinx

=> 0 = - sinx

=> sin0° = - sinx

=> x = 0°

Hence,

x = 0°

Verification,

√2cos (45 + 0) = cos0 - sin0

=> √2 cos45 = 1 - 0

=> √2 × 1/√2 = 1

=> 1 = 1

L.H.S = R.H.S, verified.