. Find the value of expression

If xcos A – y sinA = 1 and xsinA+ ycosA = 4, then the value of 17x² + 17y² is:

A. 49

B. 289

C. 7

D. 0

Best Answer

Correct Option is : B

Solution :

We have

(xcos A – y sinA)² = 1

⇒ x²cos²A + y²sinA² -2xcosAysinA = 1

Also by, xsinA+ ycosA = 4

⇒ x²sin²A +y² cos²A + 2xsinAycosA = 16

Adding the two equations we get:

(x² +y²) = 1+ 16 = 17

Then 17x² + 17y² = 17(17) = 289

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