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3 years ago

If tanA = 1/2 then evaluate cos A/sinA +sinA /1+cosA

Mathematics

1 answer:

Deffense [45]3 years ago

3 0

Answer:

√5.

Step-by-step explanation:

Tan A = 1/2 means that the right triangle containing angle A has legs of length 1 and 2 units. So the hypotenuse = √(1^2 + 2^2) = √5 (using the Pythagoras theorem). The side opposite to < A = 1 unit and the adjacent side = 2 (as tan = opposite / adjacent).

so cos A = adjacent / hypotenuse = 2/√5.

and sin A = opposite / hypotenuse = 1 / √5

cos A / sin A = 2/√5 / 1/ √5 = 2.

sin A / (1 + cos A) = 1/√5 (1 + 2/ √5)

= 1 / √5 ( (√5 + 2) /√5)

= 1 / (√5 + 2)

So the answer is:

2 + 1 /(√5 + 2).

We can simplify it further by multiplying top and bottom of the fraction by the complement of √5 + 2 which is √5 - 2.

2 + 1 / (√5 + 2)

= 2(√5 + 2) + 1 / (√5 + 2 )

= { 2(√5 + 2) + 1 } / (√5 + 2)

Multiplying this by √5 - 2 / √5 - 2 we get:

(2(5 - 4) + √5 - 2) / (5 -4)

= 2 + √5 - 2 / 1

= √5.

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Step-by-step explanation:

From the question, we are informed that there were 600 performers in a dance recital and that the ratio of men to women is 4:6.

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3 years ago

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.917 g and a standard deviation

Nutka1998 [239]

Answer:

$z = \frac{0.872-0.917}{\frac{0.303}{\sqrt{37}}}= -0.903$

And we can find this probability to find the answer:

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And using the normal standar table or excel we got:

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Step-by-step explanation:

Let X the random variable that represent the amounts of nocatine of a population, and for this case we know the distribution for X is given by:

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Where $\mu=0.917$ and $\sigma=0.303$

We have the following info from a sample of n =37:

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And we can use the z score formula given by;

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$P(z$

And using the normal standar table or excel we got:

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3 years ago

0.134 bar in the form of p/q

kenny6666 [7]

Answer:

67/500

Step-by-step explanation:

we have

The decimal number 0.134

Convert to a fraction number

Multiply by (1,000/1,000) the number

0.134*(1,000/1,000)=134/1,000

Simplify

Divide by 2 both numerator and denominator

67/500

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3 years ago

If tanA = 1/2 then evaluate cos A/sinA +sinA /1+cosA​

If tanA = 1/2 then evaluate cos A/sinA +sinA /1+cosA