Question

value of x for sin2x+cos4x=2

Answer 1

hey there will be no value of x which will satisfy this equation.

Answer 2

$x=\dfrac{\pi}{12}$

Step-by-step explanation:

We have,

$\sin 2x+\cos 4x=2$

To find, the value of x = ?

∴ $\sin 2x+\cos 2(2x)=2$

⇒ $\sin 2x+1-2\sin^2 2x=2$

[ ∵$\cos2A=1-2\sin^2 A$]

⇒ $2\sin^2 2x-\sin 2x+1=0$

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

⇒$\sin^2 2x-2\dfrac{1}{2} \sin 2x+\dfrac{1}{2} +\dfrac{1}{4}-\dfrac{1}{4} =0$

⇒$(\sin 2x-\dfrac{1}{2})^{2} +\dfrac{1}{2} -\dfrac{1}{4} =0$

⇒$(\sin 2x-\dfrac{1}{2})^{2} +\dfrac{1}{4} =0$

⇒ $\sin 2x-\dfrac{1}{2}=0$

⇒ $\sin 2x=\dfrac{1}{2}=\sin \dfrac{\pi}{6}$

⇒ $2x=\dfrac{\pi}{6}$

⇒ $x=\dfrac{\pi}{12}$

∴ $x=\dfrac{\pi}{12}$