2 sin 2 β+4 cos (α+β) ⋅ sin α ⋅ sin β+ cos 2(α+β) is equal to

Question

2 sin 2 β+4 cos (α+β) ⋅ sin α ⋅ sin β+ cos 2(α+β) is equal to (A)  sin 2 α (B)  cos 2 α (C)  tan 2 α (D)  cot 2 α

Tardigrade Admin · Accepted Answer

2 sin 2 β+4 cos (α+β) sin α sin β+ cos 2(α+β) =2 sin 2 β+4( cos α cos β- sin α sin β) sin α sin β +( cos 2 α cos 2 β- sin 2 α sin 2 β) = 2 sin 2 β+4 sin α cos α sin β cos β-4 sin 2 α sin 2 β + cos 2 α cos 2 β- sin 2 α sin 2 β = 2 sin 2 β+ sin 2 α sin 2 β-4 sin 2 α sin 2 β + cos 2 α cos 2 β- sin 2 α sin 2 β = (1- cos 2 β)-(2 sin 2 α)(2 sin 2 β)+ cos 2 α cos 2 β = (1- cos 2 β)-(1- cos 2 α)(1- cos 2 β)+ cos 2 α cos 2 β = cos 2 α

Q. $2 sin^{2} β + 4 cos (α + β) \cdot sin α \cdot sin β + cos 2 (α + β)$ is equal to

$sin 2 α$

$cos 2 α$

$tan 2 α$

$cot 2 α$

Q. 2sin2β+4cos(α+β)⋅sinα⋅sinβ+cos2(α+β) is equal to

sin2α

cos2α

tan2α

cot2α

Q. $2 sin^{2} β + 4 cos (α + β) \cdot sin α \cdot sin β + cos 2 (α + β)$ is equal to

$sin 2 α$

$cos 2 α$

$tan 2 α$

$cot 2 α$