If x CosA - y SinA = 1 and x SinA + y CosA = 4, then the value of 17x2 + 17y2 is :
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Correct answer: D
Explanation
The correct answer is option 4 i.e 289
Explanation:
x CosA - y SinA = 1
Take the square of both sides,
(x CosA - y SinA)2 = 1
(x CosA)2 - 2xy SinA CosA + (y SinA)2 = 1 ------(1)
(∵(a + b)2 = a2 + b2 + 2ab)
x SinA + y CosA = 4
Take the square of both sides,
(x SinA + y CosA)2 = 16
(x SinA)2 + 2xy SinA CosA + (y CosA)2 = 16 ------(2)
Addition of eq(1) and eq(2),
(x CosA)2 + (x SinA)2 + (y SinA)2 + (y CosA)2 = 17
x2 + y2 = 17
17x2 + 17y2 = 17 × 17
17x2 + 17y2 = 289