Question

Show that 2 sin 2 β + 4 cos(α + β) sin α sin β + cos 2(α + β) = cos 2α Please answer as soon as possible.

Answer 1

Step-by-step explanation:

LHS = 2 sin2 β + 4 cos (α + β) sin α sin β + cos 2(α + β)

= 2 sin2 β + 4 (cos α cos β – sin α sin β) sin α sin β + (cos 2α cos 2β – sin 2α sin 2β)

= 2 sin2 β + 4 sin α cos α sin β cos β – 4 sin2 α sin2 β + cos 2α cos 2β – sin 2α sin 2β

= 2 sin2 β + sin 2α sin 2β – 4 sin2 α sin2 β + cos 2α cos 2β – sin2α sin2β = (1 – cos 2β) – (2 sin2 α) (2 sin2 β) + cos 2α cos 2β

= (1 – cos 2β) – (1 – cos 2α) (1 – cos 2β) + cos 2α cos 2β

= cos 2α

Answer 2

Step-by-step explanation:

LHS = 2 sin2 β + 4 cos (α + β) sin α sin β + cos 2(α + β)

= 2 sin2 β + 4 (cos α cos β – sin α sin β) sin α sin β + (cos 2α cos 2β – sin 2α sin 2β)

= 2 sin2 β + 4 sin α cos α sin β cos β – 4 sin2 α sin2 β + cos 2α cos 2β – sin 2α sin 2β

= 2 sin2 β + sin 2α sin 2β – 4 sin2 α sin2 β + cos 2α cos 2β – sin2α sin2β = (1 – cos 2β) – (2 sin2 α) (2 sin2 β) + cos 2α cos 2β

= (1 – cos 2β) – (1 – cos 2α) (1 – cos 2β) + cos 2α cos 2β

= cos 2α

PLEASE MARK AS BRAINLIEST ANSWER AND FOLLOW ME PLEASE PLEASE PLEASE