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

link

Prove the converse of the Pythagorean Theorem

link

Use Pythagoras' theorem

link

the triangle angle

link

Keywords: trigonometric identities, sin, cos

step-by-step explanation: