If 'x' = 3cos A + 4sin A and 'y' = 3sin A - 4cos A, then find the value of 2(x² + y²).
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Correct answer: A
Explanation
Has been given :
x = 3cosA + 4sinA
y = 3sinA − 4cosA
According to the formula:
sin²A + cos²A = 1
x² = (3cosA + 4sinA)²
= 9cos²A + 16sin²A + 24sinAcosA
y² = (3sinA − 4cosA)²
= 9sin²A + 16cos²A − 24sinAcosA
x² + y²= (9cos²A + 16sin²A + 24sinAcosA)
(9sin²A + 16cos²A − 24sinAcosA)
= 9(cos²A + sin²A) + 16(sin²A + cos²A)
= 9 + 16
= 25
2(x² + y²)= 2 × 25= 50