Question

10. If acos - b sin 0 = x and a sin 0 + b cos 0 = y, find x2+y2.​

Answer 1

Correct Question:-

If acos ø - b sin ø = x and a sin ø + b cos ø = y, find x²+y².

Solution:-

We have :

x= a cos ø -b sin ø

Squaring both side we get

x²=(a cos ø-b sin ø) ²

x² a² cos² ø+b² sin² ø -2 ab cos ø sin ø ---(1)

Now,

y= a sin ø + b cos ø

Squaring both side we get

y²=(a sin ø+b cos ø) ²

y²=a² sin² ø+b² cos² ø +2 ab cos ø sin ø ---(2)

Now adding both equation , we get

x²+y²= a² cos² ø+b² sin² ø -2 ab cos ø sin ø+a² sin² ø+b² cos² ø +2 ab cos ø sin ø

x²+y²= a²cos ²ø+a²sin²ø+ b²cos ²ø+b²sin²ø

x²+y²= a²( cos²ø+sin²ø) +b²( cos²ø +sin ²ø)

Now we know that sin²A+cos²A=1 where value of A is any value for both

thus ,

x²+y²=a²+b²

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Answer 2

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