Question

If a cos theta + b sin theta is equal to 4 and a sin theta minus b cos theta is equal to 3 find a square + b square

Answer 1

a cos(theta) + b sin(theta)=4...............(1)
a sin(theta) - b cos(theta) =3...............(2)

squaring both the sides of equation 1 - we get
a²cos²(theta) + b²sin²(theta) +2ab cos(theta)sin(theta) = 16 .......(3)

squaring both the sides of equation 2
a²sin²(theta) +b²cos²(theta) -2ab cos(theta)sin(theta) = 9 .............(4)

adding (3) and (4) .. we get
a²cos²(theta) + b²sin²(theta) + a²sin²(theta) +b²cos²(theta) = 25
a²[cos²(theta) + sin²(theta) ] +b²[cos²(theta) + sin²(theta) ] = 25
a²(1) +b²(1) =25
a²+ b² =25

Answer 2

25 is your answer, Okyyyyyyyyyyy