Question

використовуючи формулу зниження степіння​

Answer 1

$\displaystyle\bf\\2Sin^{2} 4x\geq 0,5\\\\\\2\cdot\frac{1-Cos8x}{2} \geq 0,5\\\\\\1-Cos8x\geq 0,5\\\\-Cos8x\geq -0,5\\\\Cos8x\leq 0,5\\\\\\\frac{\pi }{3} +2\pi n\leq 8x\leq \frac{5\pi }{3} +2\pi n,n\in Z\\\\\\\frac{\pi }{24} +\frac{\pi n}{4} \leq x\leq \frac{5\pi }{24}+\frac{\pi n}{4}, n\in Z \\\\\\Otvet:x\in\Big[\frac{\pi }{24} +\frac{\pi n}{4} \ ; \ \frac{5\pi }{24} +\frac{\pi n}{4} \Big],n\in Z$

При решении была применена формула понижения степени :

$\displaystyle\bf\\Sin^{2} x=\frac{1-Cos2x}{2}$

Answer 2

Using the Power Reduction Formula

The power reduction formula is a trigonometric identity that allows us to express a trigonometric function in terms of another trigonometric function. It is particularly useful when dealing with higher powers of trigonometric functions.

The power reduction formula for cosine is given by:

cos^2(x) = (1 + cos(2x)) / 2 This formula allows us to reduce the power of cosine from 2 to 1, which can simplify calculations and expressions involving trigonometric functions.

Similarly, the power reduction formula for sine is given by:

sin^2(x) = (1 - cos(2x)) / 2 This formula allows us to reduce the power of sine from 2 to 1.

By using these power reduction formulas, we can simplify trigonometric expressions and solve trigonometric equations more easily.

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