prove that: sinA/1+cosA +cosA/sinA=cosecA​

Answers

Answer 1

Answer:

We proceed to demonstrate the identity given on statement by algebraic and trigonometric means:

1) [tex]\frac{\sin A}{1 + \cos A} + \frac{\cos A}{\sin A}[/tex] Given

2) [tex]\frac{\sin^{2}A+\cos A\cdot (1+\cos A)}{\sin A\cdot (1 + \cos A)}[/tex]  [tex]\frac{a}{b} + \frac{c}{d} = \frac{a\cdot d + b\cdot c}{b\cdot d}[/tex]/Definition of power

3) [tex]\frac{\sin^{2}A+\cos^{2}A + \cos A}{\sin A\cdot (1 + \cos A)}[/tex] Distributive property/Definition of power

4) [tex]\frac{1+\cos A}{\sin A\cdot (1+\cos A)}[/tex] Associative property/[tex]\sin^{2}A + \cos^{2}A = 1[/tex]

5) [tex]\frac{1}{\sin A}[/tex] Existence of multiplicative inverse/Modulative property

6) [tex]\csc A[/tex]     [tex]\frac{1}{\sin A} = \csc A[/tex]/Result

Explanation:

We proceed to demonstrate the identity given on statement by algebraic and trigonometric means:

1) [tex]\frac{\sin A}{1 + \cos A} + \frac{\cos A}{\sin A}[/tex] Given

2) [tex]\frac{\sin^{2}A+\cos A\cdot (1+\cos A)}{\sin A\cdot (1 + \cos A)}[/tex]  [tex]\frac{a}{b} + \frac{c}{d} = \frac{a\cdot d + b\cdot c}{b\cdot d}[/tex]/Definition of power

3) [tex]\frac{\sin^{2}A+\cos^{2}A + \cos A}{\sin A\cdot (1 + \cos A)}[/tex] Distributive property/Definition of power

4) [tex]\frac{1+\cos A}{\sin A\cdot (1+\cos A)}[/tex] Associative property/[tex]\sin^{2}A + \cos^{2}A = 1[/tex]

5) [tex]\frac{1}{\sin A}[/tex] Existence of multiplicative inverse/Modulative property

6) [tex]\csc A[/tex]     [tex]\frac{1}{\sin A} = \csc A[/tex]/Result


Related Questions

+ 12 POINTS PLZZ HELLLP

Answers

The correct answer is D. Assigning representatives to control different provinces.

Explanation

Chandragupta Maurya was a Maurya leader who managed to unify much of the territory of the Indian subcontinent. During his mandate, he defeated several Greek armies motivated by the conquest of new territories in Asia. In addition, he meant an improvement in economic activities, internal and external trade, and agriculture. In the administrative aspect, he stood out for delegating governance responsibilities to representatives who controlled different provinces to provide security to the population because the size of the Empire's territory prevented him from governing from a center of power, so he had to delegate powers to avoid weakness throughout the territory. Therefore, the correct answer is D. Assigning representatives to control different provinces.

What kind of landform is found in
a divergent boundary at the
bottom of the ocean?​

Answers

Answer:

Most divergent plate boundaries are underwater and form submarine mountain ranges called oceanic spreading ridges. While the process of forming these mountain ranges is volcanic, volcanoes and earthquakes along oceanic spreading ridges are not as violent as they are at convergent plate boundaries.

Tuberculosis, a respiratory infection is often caused by AIDS?
True
False

Answers

Answer:

How is tuberculosis related to AIDS?

HIV weakens the immune system, increasing the risk of TB in people with HIV. Infection with both HIV and TB is called HIV/TB coinfection. Untreated latent TB infection is more likely to advance to TB disease in people with HIV than in people without HIV.

False because AIDS forms from HIV which weakens your immune system although since your immune system is weak you could easily get tuberculosis

Tell whether the side lengths 3,9, and 15 form a triangle.

Answers

Answer: No, because 9 + 3 isn’t greater than 15.

Explanation:

According to the triangle inequality theorem, the sun of the 2 shorter legs of a triangle must add up and be greater than the longest side of the triangle which is the hypotenuse.

Therefore, in this case, the addition of 3 and 9 which is 12 is less than 15, therefore, the side lengths doesn't make a triangle.

Does climate change cause global warming ?

Answers

Answer:

Global warming refers only to the Earth's rising surface temperature, while climate change includes warming and the “side effects” of warming.

Explanation:

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