If $sin A + {sin}^{2} A = 2,$ then the value of $cos A + {cos}^{2} A + {cos}^{4} A$ is

Open in App

Solution

$sin A + {sin}^{2} A = 2 \Rightarrow {sin}^{2} A + sin A - 2 = 0 \Rightarrow (sin A + 2) (sin A - 1) = 0 \Rightarrow sin A = 1 (∵ sin A \in [- 1, 1]) \Rightarrow cos A = \sqrt{1 - {sin}^{2} A} = 0$

Therefore,
$cos A + {cos}^{2} A + {cos}^{4} A = 0$

Suggest Corrections

Similar questions

\frac{sin A + sin 2 A + sin 4 A + sin 5 A}{cos A + cos 2 A + cos 4 A + cos 5 A} =

If $sin A + {sin}^{2} A = 1$ Then, $({cos}^{2} A + {cos}^{4} A) = ?$

\frac{c o s 3 A - c o s A}{s i n 3 A - s i n A} + \frac{c o s 2 A - c o s 4 A}{s i n 4 A - s i n 2 A} =

\frac{sin A}{cos 2 A cos 3 A}

sin A + {sin}^{2} A = 1

{cos}^{2} A + {cos}^{4} A = 1

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program