Question

if sin= ½ find 4 cos³ a- 3cos a​

Answer 1

value of 4cos3A - 3cosA = 0

it is given that, sinA = 1/2

we know, sin30° = 1/2

so, sinA = 1/2 = sin30°

⇒A = 30°

now we have to find 4cos³A - 3cosA

this can be solved by two methods. let me explain you.

1st method : putting, A = 30°

4cos³(30°) - 3cos(30°)

we know, cos30° = √3/2

so, 4(√3/2)³ - 3(√3/2) = 4 × 3√3/8 - 3√3/2

= 3√3/2 - 3√3/2 = 0

2nd method : using formula, cos3Φ = 4cos³Φ - 3cosΦ

here, 4cos³A - 3cosA = cos3A

now putting, A = 30°

we get, cos3(30°) = cos90° = 0

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