$2 {cos}^{3} A sin A + 2 {sin}^{3} A cos A$ equals which one of the following?

cos 2 A

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 sin A

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 cos A

No worries! We‘ve got your back. Try BYJU‘S free classes today!

{cos}^{2} A

No worries! We‘ve got your back. Try BYJU‘S free classes today!

sin 2 A

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $sin 2 A$
The value of $2 {cos}^{3} A sin A + 2 {sin}^{3} A cos A$
$= 2 sin A cos A ({cos}^{2} A + {sin}^{2} A)$
$= 2 sin A cos A$
$= sin (2 A)$

Suggest Corrections

Similar questions

s i n^{2} A = c o s^{2} (A + B) + c o s^{2} B - 2 c o s (A - B) c o s A c o s B

{sin}^{2} A = {cos}^{2} (A - B) + {cos}^{2} B - 2 cos (A - B) cos A cos B

Which of the following options are equal to ${cos}^{2} A - {sin}^{2} A$ ?

\frac{{sin}^{2} A}{{cos}^{2} A} + \frac{{cos}^{2} A}{{sin}^{2} A} = {sec}^{2} A c o s e c^{2} A - 2

\frac{{sin}^{2} A}{{cos}^{2} A} + \frac{{cos}^{2} a}{{sin}^{2} A} = \frac{1}{{sin}^{2} A {cos}^{2} A} - 2

Join BYJU'S Learning Program