Question

The solutions of the equation $4co{s}^{2}x+6si{n}^{2}x=5$ are

• A. x = nπ ± π / 4, nϵZ
• B. x = nπ ± π /3, nϵZ
• C. x = nπ ± π /2, nϵZ
• D. x = nπ ± 2π /3, nϵZ

Answer 1

The correct option is A

x = nπ ± π / 4, nϵZ

$Given,4co{s}^{2}x+6si{n}^{2}x=5\Rightarrow 4(co{s}^{2}x+si{n}^{2}x)+2si{n}^{2}x=5\Rightarrow 2si{n}^{2}x=5-4\Rightarrow si{n}^{2}x=\frac{1}{2}\Rightarrow x=n\pi \pm \frac{\pi }{4},n\in Z$