Question

IF 8sinA=4+cosA Find sinA

Answer 1

Hi,

Here is your answer !
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8sinA = 4 + cosA

=> 8sinA - 4 = cosA

Squaring both sides , We get

(8sinA - 4)² = cos²A

64sin²A - 64sinA + 16 = 1 - sin²A

64sin²A + sin²A - 64sinA + 16 - 1 = 0

65sin²A - 64sinA + 15 = 0

Let x = sinA , We have

65x² - 64x + 15 = 0

65x² - 39x - 25x + 15 = 0

13x (5x - 3) - 5 (5x - 3) = 0

(5x - 3) (13x - 3) = 0

=> 5x - 3 = 0 or 13x - 3 = 0

=> x = 3/5 or x = 3/13

=> sinA = 3/5 or sinA = 3/13

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Formula used :

=> (a + b)² = a² + 2ab + b²

=> sin²x + cos²x = 1