If x = 7sin A + 24cos A and y = 7cos A - 24sin A, then what is the value of 3(x² + y²)?
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Correct answer: C
Explanation
Has been given :
x = 7sinA + 24cosA
y = 7cosA − 24sinA
According to the formula:
sin²A + cos²A = 1
x² + y²= (7sinA + 24cosA)² + (7cosA − 24sinA)²
= 49sin²A + 336sinAcosA + 576cos²A
49cos²A − 336sinAcosA + 576sin²A
= 49(sin²A + cos²A) + 576(sin²A + cos²A)
= (49 + 576)(sin²A + cos²A)
= 625 × 1
= 625
3(x² + y²)= 3 × 625= 1875