If $x=4 \cos A+5 \sin A$ and $y=4 \sin A-5 \cos A$, then the value of $x^2+y^2$ is:
Answer & explanation
Correct answer: option 1
x = 4cosA + 5sinA
On squaring both side ,
x² = ( 4cosA + 5sinA )²
x² = 16cos²A + 25sin²A + 40sinA.cosA ------(1)
And, y = 4sinA - 5cosA
on squaring both side,
y² = ( 4sinA + 5cosA )²
y² = 16sin²A + 25cos²A - 40sinA.cosA -------(2)
On adding equation 1 and 2.
x² + y² = 16 ( sin²A + cos²A ) + 25 ( sin²A + cos²A )
{ using, sin²A + cos²A = 1 }
x² + y²
= 16 + 25
= 41