Question

4 If x = 4cosA + 5sinA and y = 4sinA - 5 cosa, then the value of x2 + y2 is:
X 1.25
X 2. 16
X 3.0
√ 4.41​

Answer 1

Step-by-step explanation:

x² + y²

= (4CosA + 5SinA)² + (4SinA-5CosA)²

= (16Cos²A+25Sin²A+40SinA*CosA) + (16Sin²A+25Cos²A-40SinA*CosA)

= 16(Cos²A+Sin²A)+25(Sin²A+Cos²A) + 0

= 16*1 + 25*1 + 0 = 16+25 = 41

Answer 2

The value of $x^2+y^2$ is 41.

Step-by-step explanation:

Given :

$x=4\cos A + 5\sin A$

$y=4\sin A - 5\cos A$

To find :

$x^2+y^2$

Solution,

$x^2+y^2\\\\=(4\cos A + 5\sin A)^2+(4\sin A - 5 \cos A)^2$

Using identity $(a+b)^2$ and $(a-b)^2$ We iwill get :

$=(4\cos A + 5\sin A)^2+(4\sin A - 5 \cos A)^2\\\\=16\cos^2A+25\sin^2A+40\cos A\sin A+16\sin^2 A+25\cos A^2-40\sin A\cos A\\\\=41\cos^2A+41\sin^2 A+0$

Since, $\cos^2 A+\sin ^2A=1$

So,

$=41\cos^2A+41\sin^2 A\\\\=41(\cos^2A+\sin^2 A)\\\\=41\times 1\\\\=41$

So, the value of $x^2+y^2$ is 41. Hence, the correct option is (D).