If $x \cos A-y \sin A=1$ and $x \sin A+y \cos A=4$, then the value of $17 x^2+17 y^2$ is:
Answer & explanation
Correct answer: option 4
We are given that ,
x cosA - y sinA = 1
& x sinA + y cosA = 4
Square both the equations and then add,
x²cos²A + y²sin²A - 2xcosA.ysinA + x²sin²A + y²cos²A + 2xcosA.ysinA
= 1 + 16
x² (sin²A + cos²A ) + y² ( sin²A + cos²A ) = 17
{ Using , sin²A + cos²A = 1 }
x² + y² = 17
Now,
17 (x² + y² )
= 17 × 17
= 289