Question

for this I want answer

Answer 1

hello users

we have to prove
(√3 cos 23° - sin 23°) / 2 = cos 53°

solution
we know that
cos x cos y - sin x sin y = cos(x+y)
And
cos 30° = √3/2 , sin 30° = 1/2

Here
Taking L.H.S 
(√3 cos 23° - sin 23°) /2 

= √3/2 * cos 23° - 1/2 * sin 23°

= cos 30° *cos 23° - sin 30° * sin 23°

= cos ( 30° + 23°)

= cos 53° = R.H.S

Hence 
proved L.H.S = R.H.S

@ hope it helps :)