You visited us 1 times! Enjoying our articles? Unlock Full Access!

General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2

The number of...

Question

The number of solution(s) of $sin 2 x + cos 4 x = 2$ in the interval $(0, 2 π)$ is

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

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

Open in App

Solution

The correct option is B 0
$sin 2 x + cos 4 x = 2$

$\Rightarrow sin 2 x + 1 - 2 {sin}^{2} 2 x = 2$

$\Rightarrow 2 {sin}^{2} 2 x - sin 2 x + 1 = 0$

this is a quadratic equation in $sin 2 x$

Discriminant $D = (- 1)^{2} - 4 (2) (1) = 1 - 8 = - 7 < 0$

since $D, 0$ the quadratic equation has non-real roots.

Hence, for $sin 2 x + cos 4 x = 2$ there are no real solutions

$∴$ option A is correct.

Suggest Corrections

Similar questions

{cos}^{4} x + \frac{1}{c o s^{2} x} = s i n^{4} x + \frac{1}{s i n^{2} x}

[0, 2 π]

?

Find the number of solutions of cos(x)+cos(2x)+cos(3x)+cos(4x)+cos(5x)=5 in the interval [0,2π]

\frac{5}{4} {cos}^{2} 2 x + {cos}^{4} x + {sin}^{4} x + {cos}^{6} x + {sin}^{6} x = 2

[0, 2 π]

\frac{5}{4} c o s^{2} 2 x + c o s^{4} x + s i n^{4} x + c o s^{6} x + s i n^{6} x = 2

[0, 2 π]

sin 2 x + cos 4 x = 2

Join BYJU'S Learning Program