Thank you for the interesting question, this is how I approached it after doing a quick ponder on the left side I thought it would be long and decided to start on the right. You can turn the cos^2(x) into a 1-sin^2(x). Then turn the sin^2(x) into (1-cos(2x))/2. Then simplify the 1-(1-cos(2x))/2 into 1/2+cos(2x)/2. Multiply by 4 to give you 2+2cos(2x). Then multiply by cos(3x) to get you 2cos(3x)+2cos(2x)cos(3x). using the formula for cos(a+b) and cos(a-b) we can say that cos(a+b)+cos(a-b)=2cos(a)cos(b) we can apply this to our 2cos(2x)cos(3x) to make it a cos(3x-2x) + cos(3x+2x) which is cos(x)+cos(5x). Therefore our overall term is 2cos(3x)+cos(x)+cos(5x) which equals the left hand side. If any mistakes, please say and sorry for the horrendous looking format.
4 lines is all it took,
LHS=2 cos2X.cosX + 2 cos4XcosX
=2cosX(cos2X+cos4X)
=2cosX(2cos3XcosX)
=4cos3Xcos^2 X
=RHS
Thank you for the interesting question, this is how I approached it after doing a quick ponder on the left side I thought it would be long and decided to start on the right. You can turn the cos^2(x) into a 1-sin^2(x). Then turn the sin^2(x) into (1-cos(2x))/2. Then simplify the 1-(1-cos(2x))/2 into 1/2+cos(2x)/2. Multiply by 4 to give you 2+2cos(2x). Then multiply by cos(3x) to get you 2cos(3x)+2cos(2x)cos(3x). using the formula for cos(a+b) and cos(a-b) we can say that cos(a+b)+cos(a-b)=2cos(a)cos(b) we can apply this to our 2cos(2x)cos(3x) to make it a cos(3x-2x) + cos(3x+2x) which is cos(x)+cos(5x). Therefore our overall term is 2cos(3x)+cos(x)+cos(5x) which equals the left hand side. If any mistakes, please say and sorry for the horrendous looking format.
15 mins for a question is crazy
You guys have it easy rn
I got another solution
Cosx + cos5x+ 2cos3x
=2cos((5x+x)/2)cos((5x-x)/2)+ 2cos3x
=2cos 3x cos2x+ 2cos3x
=2cos3x(cos2x+1)
=2cos3x((2(cosx)^2)-1+1)
=4cosx^2.cos3x
This is far quicker but unfortunately not in the A-Level specification anymore
But sir as we already got the solution,and there's no mistake in this so what's the need to worry about specifications?
Thank you bro, follow doing this bro, follow your dream
Noicéêë
clipped 7:24
Oh hell nahhhhh 😂😂😂😂
FYI take cosx +xos3x +cos3x+cos5x and solve it’ll be much easier
I have a shorter soln, cud any1 guide me how to contact Mr.Neil?
Me also
Sir can you please do tutorial on the whole topic of trig identies
Yep I'll be releasing over time
@NeilDoesMaths thank you sir coz l do add maths and its giving me quite a challenge
Wow that was tricky
Trust me. My brain was deteriorating
Wait
As a year 9, I am confusion 💀
You'll get it on day
Next lesson I'll do it with you guys
@@NeilDoesMaths yay
Sir you lied 😢
@ fr
Lost!
Gramp cooking too much 🤕
Man like Hasan