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Trigonometrical Equations
easy
The number of solution of the given equation $a\sin x + b\cos x = c$ , where $|c|\, > \,\sqrt {{a^2} + {b^2}} ,$ is
A
$1$
B
$2$
C
Infinite
D
None of these
Solution
(d) $\frac{a}{{\sqrt {{a^2} + {b^2}} }}\sin x + \frac{b}{{\sqrt {{a^2} + {b^2}} }}\cos x = \frac{c}{{\sqrt {{a^2} + {b^2}} }}$
$\sin (x + \alpha ) = \frac{c}{{\sqrt {{a^2} + {b^2}} }} > 1$, (as given)
Hence there is no solution.
Standard 11
Mathematics
