(xsinA-ysinA)^2(XcosA+ysinA)^2=x^2+y^2
nickkaushiknick:
there should be "+" in between two given brackets.
infact it should be (x sin A - y cos A)^2 + (x cos A + y sin A)^2, please check
yeah sorry so please do this
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Here LHS
(x sin A - y cos A)² + (x cos A + y sin A)²
Expending brackets using (a + b)² and (a - b)²
[(xsinA)² - 2(xsinA) (ycosA) + (y cosA)² ] + [(xcosA)² + 2(xcosA) (ysinA) + (ysinA)²]
x²sin²A - 2xysinAcosA + y²cos²A + x²cos²A + 2xycosAsinA + y²sin²A
x²sin²A + x²cos²A + y²sin²A + y²cos²A
x²( sin²A + cos²A) + y² (sin²A + cos²A)
x² × 1 + y² × 1 [∵ sin²Ф + cos²Ф =1]
x² + y² = RHS
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