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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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<h2>Solving Equations</h2>

To solve linear equations, we must perform inverse operations on both sides of the equal sign to <em>cancel values out</em>.

If something is being added to x, subtract it from both sides.
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Same with multiplication and division. If x is being divided, multiply. If x is being multiplied, divide.

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<h2>Solving the Questions</h2><h3>Question 1</h3>

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Because 7 is being added to x, subtract it from both sides:

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Because x is being multiplied by 5, divide both sides by 5:

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Therefore. $x=\dfrac{8}{5}$ .

<h3>Question 2</h3>

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In the past, the population proportion of consumers preferring orange juice with no pulp was equation. To test if this populatio

geniusboy [140]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

a) For the null hypothesis,

P = 0.45

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b) For the decision rule, we would reject H0 if 0.1 > p value and accepth H0 if 0.1 < p value

Considering the population proportion, probability of success, p = 0.45

q = probability of failure = 1 - p

q = 1 - 0.45 = 0.55

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c) We would determine the test statistic which is the z score

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Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.45 - 0.02 = 0.43

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d) Since alpha, 0.1 < than the p value, 0.67, then we would fail to reject the null hypothesis. Therefore, at a 1% level of significance, we do not have enough evidence to reject the null hypothesis

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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