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General Solution of Trigonometric Equation

If 0 ≤ x ≤ ...

Question

If $0 \leq x \leq 2 π$ , then the number of solution of $3 (sin x + cos x) - 2 ({sin}^{2} x + {cos}^{2} x) = 8$ is:

0

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Solution

The correct option is D $0$
$3 (s i n x + c o s x) - 2 (s i n^{2} x + c o s^{2} x) = 8$
$3 (s i n x + c o s x) - 2 (1) = 8$
$3 (s i n x + c o s x) = 10$
$s i n x + c o s x = \frac{10}{3}$
Therefore,
$- 1 \leq s i n θ \leq 1$ and $- 1 \leq c o s x \leq 1$
Implies that,
$- 2 \leq s i n x + c o s x \leq 2$
Hence no value of $x$ exist.
Such that $s i n x + c o s x = \frac{10}{3}$
Therefore, it has no solution.

Suggest Corrections

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\begin{matrix} List - I & List - II (I) & Number of solutions of the equation & (P) & 0 e^{x} + e^{- x} = tan x \forall x \in [0, \frac{π}{2}) (II) & Number of solutions of the equations & (Q) & 1 x + y = \frac{2 π}{3} and cos x + cos y = \frac{3}{2} is (III) & Number of solutions of the equation & (R) & 2 cos x + 2 sin x = 1, x \in [0, 2 π) is (IV) & Number of solutions of the equation & (S) & Infinite (\sqrt{3} sin x + cos x)^{\sqrt{\sqrt{3} sin 2 x - cos 2 x + 2}} = 4 is \end{matrix}

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