Решите уравнение: Sin^4x+cos^4x=sinxcosx — MatFaq.ru

How do you verify cos4x−sin4x(2cos2x−1)2 ? cos2x Explanation: Knowing that: cos2x=cos2x−sin2x=2cos2x−1 and sin2x+cos2x=1integral of sin^4 (x) * cos^4 (x) I tried a bunch of u substitutions but nothing so far has worked.How do you use the half angle identity to find cos 105? How do you find the exact value for #sin105# using the half‐angle identity?Задача 14267 cos4x-sin4x=1... Условие. cos4x-sin4x=1. математика 10-11 класс 2599.Answer:To prove that cos 4 x − sin 4 x = 1 − 2 sin 2 x , we'll need the Pythagorean identity and a variation on the Pythagorean identity: ⇒ cos 2 x + sin 2 x …

integral of sin^4 (x) * cos^4 (x) | Free Math Help Forum

...cos x +i \sin x)^4$. Then I use the binomial theorem to expand this fourth power, and comparing real and imaginary parts, I conclude that $\begingroup$ See also: How to simplify $\sin^4 x+\cos^4 x$ using trigonometrical identities? $\endgroup...Now, there are several ways of simplifying this trigonometric expression depending on whether you want it to be in terms of sin x, cos x, tan x or multiple angles. 1st option\int (cos^{4} (x))(sin( x))dx. One Time Payment $10.99 USD for 2 months. Monthly Subscription $4.99 USD per month until cancelled.cos4(x)-sin4(x). Simplify the expression. Tap for more steps... cos2(x)-sin2(x). Apply the cosine double-angle identity.

How do you simplify cos^4x-sin^4x? | Socratic

`int sin^4 x*cos^4 x dx= int (1 - 2cos^2 2x + cos^4 2x)^2/16 dx`. Using the linearity property of integrals yields What is the integral `int cos^5 x sin^4 x dx`. 2 Educator answers.1 - 2cos^2(x) + cos^4(x) factor and use the fundamental identities to simplify. How to differentiate y=sin(4x) using the Chain Rule.Click hereto get an answer to your question(cos^4x - sin^4x) is equal to. (cos4x−sin4x) is equal to. Answer. As we know that.[math]\sin{x}=\pm\frac{\sqrt{2}}{2}[/math]. 22x\hfill\\\cos^22x=0\hfill\\\end{gathered}[/math].we know from identity that : 2sin(x).cos(x) = sin(2x). for max value of y second term must be min. which is when sin(2x) is 0, so max value is 1.

advanced research - Deriving an expression for $\cos^4 x + \sin^4 x$ - Mathematics Stack Exchange Stack Exchange Network

Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the most important, maximum relied on online neighborhood for developers to be informed, percentage their wisdom, and build their careers.

Visit Stack Exchange 0 +0 Log in Sign up

Mathematics Stack Exchange is a question and solution web page for other people finding out math at any stage and professionals in comparable fields. It simplest takes a minute to sign up.

Sign up to sign up for this group

Anybody can ask a query

Anybody can answer

The highest solutions are voted up and rise to the highest

Asked 6 years, 2 months in the past

Viewed 3k instances

$\begingroup$

Derive the id $\cos^4 x + \sin^4 x=\frac14 \cos (4x) +\frac34$

I do know $e^i4x=\cos (4x) + i \sin (4x)=(\cos x +i \sin x)^4$. Then I take advantage of the binomial theorem to enlarge this fourth power, and evaluating real and imaginary parts, I conclude that $\cos^4 x + \sin^4 x = \cos (4x) + 6 \cos^2 (x) \sin^2 (x)$.

So now I need to show that $\cos (4x) + 6 \cos^2 (x) \sin^2 (x)=\frac14 \cos (4x) +\frac34$, which has stumped me.

requested Feb 17 '15 at 15:40

DuckyDucky

1,8541616 silver badges2929 bronze badges

$\endgroup$ 1 $\begingroup$

$\cos^4x+\sin^4 x\=(\cos^2x+\sin^2x)^2-2(\sin x\cos x)^2\=1-2(\frac12\sin(2x))^2\=1-\frac12\sin^2(2x)\=1-\frac12\frac1-\cos(4x)2\=\frac14\cos(4x)+\frac34$

spoke back Feb 17 '15 at 15:45

UncountableUncountable

3,33277 silver badges1717 bronze badges

$\endgroup$ 1 $\begingroup$

$$\cos^4x+\sin^4x\=(\sin^2x+\cos^2x)^2-2\sin^2x\cos^2x\=1-\frac12\sin^22x=1-\frac12\left(\frac12(1-\cos4x)\proper)=\frac34+\frac14\cos4x$$ As: $$\sin^2x+\cos^2x=1;\(a+b)^2=a^2+b^2+2ab;\\sin2x=2\sin x\cos x;\\cos2x=\cos^2x-\sin^2x=1-2\sin^2x$$

Also: $$\cos^4x+\sin^4x=\left(\frace^ix+e^-ix2\right)^4+\left(\frace^ix-e^-ix2\right)^4\=\frac116(\small e^-4 ix+4 e^-2 ix+4 e^2 ix+e^4 ix+6+e^-4 ix-4 e^-2 ix-4 e^2 ix+e^4i x+6)\=\frac34+\frac14\left(\frace^4ix+e^-4ix2\right)=\frac34+\frac14\cos4x$$

replied Feb 17 '15 at 15:44

RE60KRE60K

17k22 gold badges2727 silver badges6969 bronze badges

$\endgroup$ 3 $\begingroup$

$$\beginalign \cos^4x + \sin^4 x &= \left( \cos^2 x \proper)^2 + \left( \sin^2 x \proper)^2 \[4pt] &= \left( \frac1 + \cos 2 x2\right)^2 + \left( \frac1-\cos 2x2 \right)^2 \[4pt] &= \frac12\left( 1 + \cos^2 2 x \right) \[4pt] &= \frac12\left( 1 + \frac1+\cos 4 x2 \right) \[4pt] &= \frac14\left(\; 3 + \cos 4 x \;\right) \endalign$$

From your explicit stopping place, you have to continue thusly: $$\startalign \cos 4 x + 6 \sin^2 x \cos^2 x &= \cos 4 x + \frac32\cdot(2\sin x \cos x)^2 \[4pt] &= \cos 4 x + \frac32\cdot \sin^2 2 x \[4pt] &= \cos 4 x + \frac32\cdot \frac1 - \cos 4 x2 \[4pt] &= \frac14\left(\;3 + \cos 4 x\;\proper) \finishalign$$

replied Feb 17 '15 at 15:51

BlueBlue

64k1111 gold badges9595 silver badges200200 bronze badges

$\endgroup$ $\begingroup$

$\cos^2 x \sin^2 x = (1 - \sin^2 x) \sin^ 2 x = \sin^2 x - \sin^ 4 x$ and via the same argument $\cos^2 x \sin^2 x = \cos^2 x - \cos^ 4 x$. Take the common of those two identities to obtain $$ \cos^2 x \sin^2 x = \frac12 - \frac\cos^4x + \sin^4 x2 \, . $$ Now change this and simplify.

responded Feb 17 '15 at 15:45

Hans EnglerHans Engler

12.8k22 gold badges2323 silver badges3838 bronze badges

$\endgroup$ Mathematics Stack Exchange works highest with JavaScript enabled

Your privacy

By clicking "Accept all cookies", you settle Stack Exchange can store cookies on your software and divulge knowledge in line with our Cookie Policy.

Accept all cookies Customize settings

OneClass: Find Dy/dx By Implicit Differentiation.5+4x=sin(xy^3)dy/dx= ?

Simple Problems In Mathematics - Notes

Untitled

Untitled

The Values Of K For Which The Equation Sin4x + Cos4x +sin2x +k = 0 Possesses Solution Is (1) K - Maths - - 3357909 | Meritnation.com

Sin^4x-cos^4x=sin^2x-cos^2x - Brainly.in

Review Exercise Set 12

The Equation Sin^4x + Cos^4x + Sin 2x + Alpha = 0 Solvable For

Fall 2011 MATH566, Homework 7

Quiz 6

Find The Intervals In Which The Function F(x) = Sin^4x + Cos^4x Is Increasing Or Decreasing Where The - Brainly.in

Answered: Question 007: Complete The Following… | Bartleby

Cos^4x$)($\sin^2x$) In Terms Of First Power Of Cosine - Mathematics Stack Exchange

Practice Test Group 4C With Solution Chapter 3

If Cos^4x/cos^2y+sin^4x/sin^2y=1 Prove That Cos^4y/cos^2x+sin^4y/sin^2x=1 - Brainly.in

Prove That Int^pi/20 Cos^4x(sin^4x + Cos^4x)dx = Pi4 .

Integrate : (sinx + Cosx)/sin^4x+cos^4x - Maths - Integrals - 6990098 | Meritnation.com

NCERT Solutions For Class 11 Maths Chapter 3 - Trigonometric Functions Exercise 3.3

Applied Differential Equations 2250

Solved: 7. The Derivative Of F(x) (cos(4x) A) 3(cos(4x) Si... | Chegg.com

6. 10. The Last Two Are Proved On Frame 2, So Tum On.