The maximum value of the function wherever it is defined is . Then is

Question

The maximum value of the function $f (x) = \frac{\sin x}{\sqrt{1 - \cos^{2} x}} + \frac{\cos x}{\sqrt{1 - \sin^{2} x}} + \frac{\tan x}{\sqrt{\sec^{2} x - 1}} + \frac{\cot x}{\sqrt{{cosec}^{2} x - 1}}$

wherever it is defined is $k$ . Then $| k |$ is

Smart Achievers · Accepted Answer

(1)

$f (x) = \frac{\sin x}{\sqrt{1 - \cos^{2} x}} + \frac{\cos x}{\sqrt{1 - \sin^{2} x}} + \frac{\tan x}{\sqrt{\sec^{2} x - 1}} + \frac{\cot x}{\sqrt{{cosec}^{2} x - 1}}$

$= \frac{\sin x}{| \sin x |} + \frac{\cos x}{| \cos x |} + \frac{\tan x}{| \tan x |} + \frac{\cot x}{| \cot x |}$ $= {\begin{matrix} 4, & x \in 1^{s t} quadrant \\ - 2, & x \in 2^{n d} quadrant \\ 0, & x \in 3^{r d} quadrant \\ - 2, & x \in 4^{t h} quadrant \end{matrix}$

$f {(x)}_{\max} = 4$

Solution

Q.
The maximum value of the function $f (x) = \frac{\sin x}{\sqrt{1 - \cos^{2} x}} + \frac{\cos x}{\sqrt{1 - \sin^{2} x}} + \frac{\tan x}{\sqrt{\sec^{2} x - 1}} + \frac{\cot x}{\sqrt{{cosec}^{2} x - 1}}$

wherever it is defined is $k$ . Then $| k |$ is

1 4

2 – 2

3 0

4 2

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Solution

Q. The maximum value of the function f(x)=sinx1-cos2x+cosx1-sin2x+tanxsec2x-1+cotxcosec2x-1 wherever it is defined is k. Then |k| is

1 4

2 – 2

3 0

4 2

Ans. (1) f(x)=sinx1-cos2x+cosx1-sin2x+tanxsec2x-1+cotxcosec2x-1 =sinx|sinx|+cosx|cosx|+tanx|tanx|+cotx|cotx|={4,x∈1st quadrant-2,x∈2nd quadrant0,x∈3rd quadrant-2,x∈4th quadrant f(x)max=4

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Q.
The maximum value of the function $f (x) = \frac{\sin x}{\sqrt{1 - \cos^{2} x}} + \frac{\cos x}{\sqrt{1 - \sin^{2} x}} + \frac{\tan x}{\sqrt{\sec^{2} x - 1}} + \frac{\cot x}{\sqrt{{cosec}^{2} x - 1}}$

wherever it is defined is $k$ . Then $| k |$ is