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The greatest and least value of \( \Large \sin x \cos\ x \) are:

A) 1, -1
B) \( \Large \frac{1}{2},\ -\frac{1}{2} \)
C) \( \Large \frac{1}{4},\ -\frac{1}{4} \)
D) 2, -2

Correct Answer:


B) \( \Large \frac{1}{2},\ -\frac{1}{2} \)

Description for Correct answer:

Let \( \Large f \left(x\right)= \sin x \cos x = \frac{1}{2}\sin 2x \)

We know \( \Large -1 \le \sin 2x \le 1 \)

=> \( \Large -\frac{1}{2} \le \frac{1}{2}\sin 2x \le \frac{1}{2} \)

Thus, the greatest and least value of \( \Large f \left(x\right) \) are

\( \Large \frac{1}{2}\ and\ -\frac{1}{2}\). respectively.

Part of solved Trigonometric ratio questions and answers : >> Elementary Mathematics >> Trigonometric ratio

Comments

Similar Questions

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A). \( \Large 1 \le A \le 2 \)

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C). \( \Large \frac{13}{16} \le A \le 1 \)

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2). \( \Large \tan \frac{2 \pi }{5} - \tan \frac{ \pi }{15} - \sqrt{3} \tan \frac{2 \pi }{5} \tan \frac{ \pi }{15} \) is equal to:

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A). \( \Large \frac{24}{25} \)

B). \( \Large -\frac{24}{25} \)

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8). The value of \( \Large \cos \frac{ \pi }{65} \cos \frac{2 \pi }{65} \cos \frac{4 \pi }{65}.....\cos \frac{32 \pi }{65} \) is

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C). \( \Large \frac{a^{2}+b^{2}-2}{2} \)

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