If x = 6cos A + 8sin A and y = 6sin A - 8cos A, find the value of x² + y².
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Correct answer: D
Explanation
Has been given :
x = 6cosA + 8sinA
y = 6sinA − 8cosA
According to the formula:
(cos²A + sin²A = 1)
x² = (6cosA + 8sinA)²
= 36cos²A + 64sin²A + 96sinAcosA
y² = (6sinA − 8cosA)²
= 36sin²A + 64cos²A − 96sinAcosA
x² + y²= (36cos²A + 64sin²A + 96sinAcosA)
(36sin²A + 64cos²A − 96sinAcosA)
= 36cos²A + 36sin²A + 64sin²A + 64cos²A
= 36(cos²A + sin²A) + 64(cos²A + sin²A)
= 36(1) + 64(1)
= 100