Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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

Sagot :

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

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.