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3 years ago

If 3a = cosec x and 3/a = cot x, find the value of 3(a2 - 1/a2)

1 answer:

3 0

$\csc(x) = \frac{r}{y} = \frac{3a}{1} \\ \cot(x) = \frac{x}{y} = \frac{3}{a} \\ y = a = 1 \\ \\ 3( {a}^{2} - \frac{1}{{a}^{2} } ) \\ 3( {1}^{2} - \frac{1}{ {1}^{2} } ) \\ = 0$

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Answer:

$\theta = 30^\circ, 330^\circ$

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Step-by-step explanation:

Given [Missing from the question]

Equation:

$cos\theta = \frac{\sqrt 3}{2}$

Interval:

$0 \le \theta \le 360$

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Required

Determine the values of $\theta$

The given expression:

$cos\theta = \frac{\sqrt 3}{2}$

... shows that the value of $\theta$ is positive

The cosine of an angle has positive values in the first and the fourth quadrants.

So, we have:

$cos\theta = \frac{\sqrt 3}{2}$

Take arccos of both sides

$\theta = cos^{-1}(\frac{\sqrt 3}{2})$

$\theta = 30$ --- In the first quadrant

In the fourth quadrant, the value is:

$\theta = 360 -30$

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So, the values of $\theta$ in degrees are:

$\theta = 30^\circ, 330^\circ$

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So, we have:

$\theta = \frac{30 * \pi}{180}, \frac{330 * \pi}{180}$

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$\theta = \frac{\pi}{6}, \frac{11\pi}{6}$

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3 years ago

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Answer:

Step-by-step explanation:

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If 3a = cosec x and 3/a = cot x, find the value of 3(a2 - 1/a2)​

If 3a = cosec x and 3/a = cot x, find the value of 3(a2 - 1/a2)