Question

find x²+y² where x and y are related as: x sin θ + y cos θ = sin θ cos θ and x sin θ = y cos θ​

Answer 1

Answer:

= 2 easy peasyyyyyyyyyyy

Answer 2

Answer:

Explanation:

x sin θ - y cos θ = 0, (Given)  

⇒ x sin θ = y cos θ  

⇒ y cos θ = x sin θ

Now dividing both sides by cos θ we get,  

y = x ∙ (sin θ/cos θ)  

Again, x sin3 θ + y cos3 θ = sin θ cos θ  

⇒ x sin3 θ + x ∙ (sin θ /cos θ) ∙ cos3 θ = sin θ cos θ [Since, y = x ∙ (sin θ/cos θ)]  

⇒ x sin θ ( sin2 θ + cos2 θ) = sin θ cos θ, [since, cos θ ≠ 0]  

⇒ x sin θ (1) = sin θ cos θ,[since, sin2 θ + cos2 θ = 0]  

⇒ x sin θ = sin θ cos θ

Now dividing both sides by sin θ we get,  

⇒ x = cos θ, [since, sin θ ≠ 0]  

Therefore, y = x ∙ (sin θ/cos θ)  

⇒ y = cos θ ∙ (sin θ/cos θ), [Putting x = cos θ]  

⇒ y = sin θ  

Now, x2 + y2  

= cos2 θ + sin2 θ  

= 1.  

Therefore, x2 + y2 = 1.

I hope this the answer :D