Question : If $2 \sin (\frac{π x}{2}) = x^{2} + \frac{1}{x^{2}}$ , then the value of $(x - \frac{1}{x})$ is:
Option 1: $- 1$
Option 2: $2$
Option 3: $1$
Option 4: $0$

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Question : If $\tan x = \frac{7}{5}$ , the value of $\frac{9 \sin x - \frac{42}{5} \cos x}{15 \sin x + 21 \cos x}$ is:
Option 1: 0
Option 2: 1
Option 3: 0.1
Option 4: 0.5

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Answer 1

Correct Answer: $0$

Solution : Given: $2 \sin (\frac{π x}{2}) = x^{2} + \frac{1}{x^{2}}$
⇒ $2 \sin (\frac{π x}{2}) = (x - \frac{1}{x})^{2} + 2$
Since $\sin θ$ has a maximum value equal to 1,
⇒ $(x - \frac{1}{x})$ = 0
Hence, the correct answer is 0.

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Question : If 2sin⁡(πx2)=x2+1x2, then the value of (x−1x) is:Option 1: –1Option 2: 2Option 3: 1Option 4: 0

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Question : If $2 \sin (\frac{π x}{2}) = x^{2} + \frac{1}{x^{2}}$ , then the value of $(x - \frac{1}{x})$ is:
Option 1: $- 1$
Option 2: $2$
Option 3: $1$
Option 4: $0$