Math, asked by rohanrj389, 1 year ago

x = cotA + cosA
y = cotA - cosA

find (x² - y²)²÷xy​

Answers

Answered by sriramiitkgp
1

Answer:

16.00 (SIXTEEN)

Step-by-step explanation:

Given:

x = cotA + cosA    ,  y = cotA - cosA

To find:

(x²-y²)² ÷ xy

solution :

(x²-y²)² ÷ xy

⇒[(x+y)²×(x-y)²] ÷ xy        ∵[(a²- b²)=(a+b)×(a-b)]

Now let us find out x+y and x-y and also xy

x + y = cotA + cosA  + cotA - cosA = 2cotA

x - y = cotA + cosA  - (cotA - cosA) = cotA + cosA - cotA + cosA = 2cosA

xy = (cotA + cosA ) × (cotA - cosA) = cot²A - cos²A

substituting the above obtained values in [(x+y)²×(x-y)²] ÷ xy we get,

⇒ [(2²×cot²A) × (2²×cos²A)] ÷ (cot²A - cos²A)   [∵2²=4]

⇒[16×cot²A×cos²A] ÷ [(cot²A)×(1 - cos²A/cot²A)]           [/ :means divided by]

numerator cot²A and denominator cot²A gets cancel

⇒(16 ×cos²A) ÷ (1 - cos²A/cot²A)

⇒(16 ×cos²A)  ÷ (1 - sin²A)          

∵[1-cos²A/cot²A = 1 - (cos²A×tan²A) = 1-cos²A ×(sin²A /cos²A) = 1-sin²A ]

⇒(16 ×cos²A)  ÷ (cos²A)    ∵[From identity : 1-sin²A = cos²A]  [1/cotA=tanA]  

⇒16

∴ (x²-y²)² ÷ xy = 16

Similar questions