Find all solutions in the interval [0, 2π . 4 sin2x - 4 sin x + 1 = 0 . pi/6, 5pi/6. pi/6, 11pi/6. pi/3, 5pi/3. 7pi/6, 11pi/6

The value of x that satisfies equation 4 sin²x - 4 sin x + 1 = 0 is π/ 6 and 5/6π

Trigonometry is the science of mathematics that studies the relationship between sides and angles in triangles

Trigonometric identity is a sentence that contains trigonometric functions. The truth of this sentence is an identity that needs to be proven

There are several types of identity formulas that can be used starting from the basic formula of the Pythagoras theorem

x² + y² = r²

This declining formula includes:

cos²a + sin²a = 1

cot²a + 1 = csc²a

1 + tan²a = sec²a

From the above equation: 4 sin²x - 4 sin x + 1 = 0, we can say sin x = a, then the equation becomes:

4a² - 4a + 1 = 0

we divide 4 :

a² - a + 1/4

then :

(a-1/2) (a-1/2) = 0

a = 1/2

so that

sin x = 1/2

Because the interval between 0 - 2π and positive sin values are in quadrants 1 and 2 so the x values that meet are 30° and 150° or π/6 and 5/6 π

trigonometric ratio

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Prove the converse of the Pythagorean Theorem

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Use Pythagoras' theorem

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the triangle angle

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Keywords: trigonometric identities, sin, cos

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !