- #1
Tanishq Nandan
- 122
- 5
Homework Statement
Integrate: 4cos(x/2).cos(x).sin(21x/2)
Homework Equations
▪sin(A+B)=sinAcosB+sinBcosA
▪2sinAcosA=sin2A
And obviously,
▪Integration of sinx is (-cosx)
▪Integration of cosx is (sinx)
The Attempt at a Solution
○I multiplied the numerator and denominator with sin(x/2)
○The numerator simplified to sin(2x)sin(21x/2) and in the denominator,we have sin(x/2).
○Now,I expanded sin(21x/2) by breaking 21x/2 into 10x and x/2 and using the above specified formula,which,on simplifying gives two terms.
○Now,the first term comes out to be sin2xcos10x,which can be integrated easily (well,maybe not one step but at least it can be done),but the second term is: sin(2x).sin(10x).cot(x/2)
How to integrate this term,it just eludes me..