Number of solutions of $3 s i n x + 4 c o s x = 10 + 4 x + x^{2}$ in the interval $[0, 2 π]$ is

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none of these

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Solution

The correct option is A 0
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y = {log}_{3} [\frac{3 sin x + 4 cos x + 10}{3 sin x + 4 cos x}]

x^{2} + 4 x + s i n^{2} x + 4 c o s e c^{2} x = 0

[0, 2 π]

\sqrt{(3 s i n x - 4 c o s x - 10) (3 s i n x + 4 c o s x - 10)}

The number of solutions of $\sum_{r = 1}^{5} c o s r x = 5$ in the interval $[0, 2 π]$ is

f (x) = (3 sin x - 4 cos x - 10) (3 sin x + 4 cos x - 10)

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