Question

If x cosA+y sin A=m and x sin A-y cos A=n then prove that square +y square =m square +n square

Answer 1

Step-by-step explanation:

ⓅⓁⒺⒶⓈⒺ ⓂⒶⓇⓀ ⒽⒶⓈ ⒷⓇⒶⒾⓃⓁⒾⒺⓈⓉ ⒶⓃⓈⓌⒺⓇ(♥_♥)(❁´◡`❁)(❁´◡`❁)(♥_♥)(❁´◡`❁)(♥_♥)

Answer 2

Given:

xcosA + ysinA = m

xsinA - ycosA = n

To find:

x² + y = m² + n²

Identities used:

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

sin²A + cos²A = 1

Solution:

RHS = m² + n²

= (xcosA + ysinA)² + (xsinA - ycosA)²

= x²cos²A + y²sinA² + 2xycosAsinA + x²sin²A + y²cosA² - 2xycosAsinA

= x²sin²A + x²cos²A + y²sinA² + y²cosA² + 2xycosAsinA - 2xycosAsinA

= x²(sin²A + cos²A) + y²(sinA² + cosA²)

= x²(1) + y²(1)

= x² + y²

Hence proved.