Mathematics: Prove the following identity. cos4 x − sin4 x = cos 2x

Prove the following identity. cos4 x − sin4 x = cos

Ответ:

kseniyayakimov

26.07.2019

$\cos^4 x - \sin^4 x = \cos 2x$ for the right-hand side, use cosine double angle identity which states that cos 2x = cos²x - sin² x $\text{rhs} = \cos 2x = \cos^2 x - \sin^2 x$ for the left-hand side $\text{lhs} = \cos^4 x - \sin^4 x$ we factor using difference of squares.recall difference of squares factoring: a² - b² = (a - b)(a + b)but here we have a⁴ - b⁴, so a⁴ - b⁴ = (a² - b²)(a² + b²)note that cos⁴ x is equivalent to (cos x)⁴ and etc. $\begin{aligned} \text{lhs} & = \cos^4 x - \sin^4 x \\ & = (\cos^2 x + \sin^2 x)(\cos^2 x - \sin^2 x) \end{aligned}$ note that cos²x + sin²x = 1 via the pythagorean identity $\begin{aligned} \text{lhs} & = \boxed{\stackrel{\text{equals to 1} }{(\cos^2 x + \sin^2 x)} }(\cos^2 x - \sin^2 x) \\ & = 1 (\cos^2 - \sin^2 x ) \\ & = \text{rhs} \end{aligned}$

0,0(0 оценок)

Ответ:

peaceouthjkdrb2398

12.01.2023

Mathematics

3x - 4y = 4

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Express the equation in slope - intercept form

y = mx + c ( m is the slope and c the y- intercept ), thus

y = $\frac{3}{4}$ x - 1

multiply through by 4

4y = 3x - 4 ( add 4 to both sides )

4y + 4 = 3x ( subtract 4y from both sides )

4 = 3x - 4y, or

3x - 4y = 4 ← in standard form

0,0(0 оценок)

Prove the following identity. cos4 x − sin4 x = cos 2x

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question