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3 years ago

Prove the following identities : i) tan a + cot a = cosec a sec a

Mathematics

1 answer:

inysia [295]3 years ago

7 0

Step-by-step explanation:

$\tan \alpha + \cot\alpha = \dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}$

$=\dfrac{\sin^2\alpha + \cos^2\alpha}{\sin\alpha\cos\alpha}=\dfrac{1}{\sin\alpha\cos\alpha}$

$=\left(\dfrac{1}{\sin\alpha}\right)\!\left(\dfrac{1}{\cos\alpha}\right)=\csc \alpha \sec\alpha$

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3 years ago

Suppose a population of honey bees in Ephraim, UT has an initial population of 2300 and 12 years later the population reaches 13

Rama09 [41]

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common ratio: 1.155

rate of growth: 15.5 %

Step-by-step explanation:

The model for exponential growth of population P looks like: $P(t)=P_i(1+r)^t$

where $P(t)$ is the population at time "t",

$P_i$ is the initial (starting) population

$(1+r)$ is the common ratio,

and $r$ is the rate of growth

Therefore, in our case we can replace specific values in this expression (including population after 12 years, and initial population), and solve for the unknown common ratio and its related rate of growth:

$P(t)=P_i(1+r)^t\\13000=2300*(1+r)^{12}\\\frac{13000}{2300} = (1+r)^12\\\frac{130}{23} = (1+r)^{12}\\1+r=\sqrt[12]{\frac{130}{23} } =1.155273\\$

This (1+r) is the common ratio, that we are asked to round to the nearest thousandth, so we use: 1.155

We are also asked to find the rate of increase (r), and to express it in percent form. Therefore we use the last equation shown above to solve for "r" and express tin percent form:

$1+r=1.155273\\r=1.155273-1=0.155273$

So, this number in percent form (and rounded to the nearest tenth as requested) is: 15.5 %

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2 years ago

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Tanzania [10]

Answer:

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3 years ago

Prove the following identities : i) tan a + cot a = cosec a sec a​

Prove the following identities : i) tan a + cot a = cosec a sec a