First slide

Trigonometric Identities

Question

Let, $f (x) = \log (\log_{1 / 3} (\log_{7} (\sin x + a)))$ be defined for every real value of x, then the possible value of a is

Moderate

A

3
B

4
C

5
D

6

Solution

$\begin{array}{ll} \log_{1 / 3} \log_{7} (\sin x + a) > 0 \\ or 0 < \log_{7} (\sin x + a) < 1 \\ or 1 < (\sin x + a) < 7, \forall x \in R \\ or 1 - \sin x < a < 7 - \sin x \end{array}$
It is found that a should be less than the minimum value of
(7 - sin x) and a must be greater than the maximum value of
(1 - sin x). Thus,
$\Rightarrow 2 < a < 6$

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