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luda_lava [24]
3 years ago
11

Evaluate cosA/2 given cosA=-1/3 and tanA >0

Mathematics
1 answer:
mote1985 [20]3 years ago
7 0

Answer:

\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}

Step-by-step explanation:

Given that:

cosA=-\dfrac{1}3

and

tanA > 0

To find:

cos\dfrac{A}{2} = ?

Solution:

First of all,we have cos value as negative and tan value as positive.

It is possible in the 3rd quadrant only.

\dfrac{A}{2} will lie in the 2nd quadrant so cos\dfrac{A}{2} will be negative again.

Because Cosine is positive in 1st and 4th quadrant.

Formula:

cos2\theta =2cos^2(\theta) - 1

Here \theta = \frac{A}{2}

cosA =2cos^2(\dfrac{A}{2}) - 1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =cosA+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =-\dfrac{1}3+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =\dfrac{2}3\\\Rightarrow cos(\dfrac{A}{2}) = \pm \dfrac{1}{\sqrt3}

But as we have discussed, cos\dfrac{A}{2} will be negative.

So, answer is:

\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}

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Let "x" be the number of times more stars are there in the universe, compared to the stars a human can see

Then from given statement,

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<em><u>Substituting given values we get,</u></em>

6 \times 10^{22} = x \times 3000\\\\x = \frac{6 \times 10^{22}}{3000}\\\\x = \frac{6 \times 10^{22}}{3 \times 10^3}\\\\x = 2 \times 10^{22-3}\\\\x = 2 \times 10^{19}

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4 years ago
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Divide by a

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