2 sin xcos x22 cos xsin x25 steps and solution pleaseSolutio

(2 sin x+cos x)^2+(2 cos xsin x)^2=5

steps and solution please

Solution

( 2sin x + cos x)² + ( 2 cos x - sin x )² = 5

LHS

[ use ( a+b)² = a² + b² + 2 ab   ( a-b)² = a² + b² - 2 ab ]

( 2sin x + cos x)² + ( 2 cos x - sin x )² :

=[ 4*sin²x + cos²x + 4*sin x*cos x ] + [ 4*cos²x + sin²x - 4*cos x*sin x]

= 4 [ sin² + cos²x] + [ cos²x + sin²x]

= 4 *1 + 1

= 5 [ cos²x + sin²x] = 1

LHS = RHS