Consider the system of equations sin x- cos 2y- a2-12-1- cos x-sin 2y- a-1- then the number of values of x- -0-2- when the system has a solution for permissible values of a is-are-

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Order of a Differential Equation

Consider the ...

Question

Consider the system of equations $sin x . cos 2 y = (a^{2} - 1)^{2} + 1, cos x . sin 2 y = a + 1$ , then the number of values of $x ϵ [0, 2 π]$ when the system has a solution for permissible values of a is/are,

1

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sin x cos 2 y = (a^{2} - 1)^{2} + 1, cos x sin 2 y = a + 1

y \in [0, 2 π]

a

sin x cos 2 y = (a^{2} - 1)^{2} + 1, cos x sin 2 y = a + 1

a

sin x cos x 2 y = (a^{2} - 1)^{2} + 1

cos x sin 2 y = a + 1

⎡ ⎢ ⎣ \begin{matrix} 2 & 1 & - 4 4 & 3 & - 12 1 & 2 & - 8 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} a 57 \end{matrix} ⎤ ⎥ ⎦

a

{cos}^{- 1} x + ({sin}^{- 1} y)^{2} = \frac{p π^{2}}{4}

({cos}^{- 1} x) ({sin}^{- 1} y)^{2} = \frac{π^{4}}{16}, p \in Z

p

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