If [ sin 2 α cos 2 α cos 2 α sin 2 α]=0, α ∈(0, π), then the values of α are

Question

If [ sin 2 α cos 2 α cos 2 α sin 2 α]=0, α ∈(0, π), then the values of α are (A) (π/2) and (π/12) (B) (π/2) and (π/6) (C) (π/4) and (3π/4) (D) (π/6) and (π/3)

Tardigrade Admin · Accepted Answer

Given, [ sin 2 α cos 2 α cos 2 α sin 2 α]=0 ⇒ sin 4 α- cos 4 α=0 ⇒ ( sin 2 α- cos 2 α)( sin 2 α+ cos 2 α)=0 ⇒ - cos 2 α(1)=0 ⇒ cos 2 α=0 ⇒ 2 α=(π/2) and (3 π/2) ⇒ α=(π/4) and (3 π/4)

Q. If $[sin^{2} α cos^{2} α cos^{2} α sin^{2} α] = 0, α \in (0, π)$ , then the values of $α$ are

$\frac{π}{2}$ and $\frac{π}{12}$

$\frac{π}{2}$ and $\frac{π}{6}$

$\frac{π}{4}$ and $\frac{3 π}{4}$

$\frac{π}{6}$ and $\frac{π}{3}$

$\frac{π}{2}$ and $\frac{π}{3}$

Q. If [sin2αcos2αcos2αsin2α​]=0,α∈(0,π), then the values of α are

2π​ and 12π​

2π​ and 6π​

4π​ and 43π​

6π​ and 3π​

2π​ and 3π​