2017年2月28日 · #int cos^4xdx = sinxcos^3x + 3int cos^2x dx -3int cos^4xdx# We have now the same integral on both sides and we can solve for it: #4 int cos^4xdx = sinxcos^3x + 3int cos^2x dx #

2018年5月23日 · cos 2x f(x) = cos^4x - sin^4 x = (cos^2 x - sin^2 x)(cos^2 x + sin^2 x) Reminder of trig identities: cos^2 x - sin^2 x = cos 2x (sin^2 x + cos^2 x) = 1 Therefor, f(x) = cos 2x

2016年12月28日 · d/dx cos^4x= -4sinxcos^3x If you are studying maths, then you should learn the Chain Rule for ...

2016年7月12日 · int (cos(x))^4 dx = 1/32[12x + 8sin(2x) + sin(4x)] While initially appearing to be a really annoying integral, we can actually exploit trig identities to break this integral down into a series of simple integrals that we are more familiar with.

The best videos and questions to learn about Proving Identities. Get smarter on Socratic.

2015年4月19日 · #cos^4(x) - sin^4(x) = cos(2x)# Remember the double angle formula for cosine: #color(blue)(cos(2x)=cos^2(x)-sin^2(x)# Plugging it into the right hand side: #cos^4(x) - sin^4(x) = cos^2(x)-sin^2(x)# Using differences of squares on the left side: #(cos^2(x) + sin^2(x)) (cos^2(x) - sin^2(x)) = cos^2(x)-sin^2(x)# And since #color(blue)(cos^2(x ...

"The fundamental trigonometric identities" are the basic identities: •The reciprocal identities •The pythagorean identities

2018年5月31日 · How do you use the power reducing formulas to rewrite the expression #cos^4x# in terms of the first power of cosine? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer

2016年6月28日 · You want to split it up using trig identities to get nice, easy integrals. cos^4(x) = cos^2(x)*cos^2(x) We can deal with the cos^2(x) easily enough by rearranging the double angle cosine formula. cos^4(x) = 1/2(1 + cos(2x))*1/2(1 + cos(2x)) cos^4(x) = 1/4(1 + 2cos(2x) + cos^2(2x)) cos^4(x) = 1/4(1 + 2cos(2x) + 1/2(1 + cos(4x))) cos^4(x) = 3/8 + 1/2*cos(2x) + 1/8*cos(4x) So, int cos^4(x) dx = 3 ...

2016年6月29日 · f^'(x)=-2sin2x Given f(x)=(cos^4x-sin^4x) =>f(x)=(cos^2x-sin^2x)(cos^2x+sin^2x) =>f(x)=(cos^2x-sin^2x)*1 =>f(x)=cos2x Differentiating w.r.to x using chain rule =>f ...