Please help me in my subject Calculus (Integrals in Trigonometric Function)

Thankyou so much in advance!

Please show complete solution because this topic is confusing me specially in getting u and du

here is example:

\fIntegrals of Trigonometric Functions Examples: IDENTITIES: (cos w + sin w )dw 5. sin20 + cos20 = 1 sin2w 1 + tan20 = sec20 COS W sin w = sin 2w dw + 1 + cot 20 = csc20 dw sin2w sin 0 tan 0 = COS W cos 0 = dw + dw sin w sin w sin w cos 0 cot ! = sin 0 = cot w cscw dw + cscw dw 1 sec 0 = cos e = - cscw - In|csc w + cotw| + C 1 CSC 0 = sin 0 1 tan 0 = cot eIntegrals of Trigonometric Functions Examples: COs 40 7 . 1 - 2sin220 Double Angle Identities: sin 20 do = do sin 20 sin 20 = 2 sin 0 cos 0 1 2sin220 = do - do cos 20 = cos20 - sin20 sin 20 sin 20 cos 20 = 2cos20 - 1 Let u = 20 cos 20 = 1 - 2sin20 du = 2do = csc 20 do - 2sin 20 do 2 tan 0 du tan 20 = 2 - do 1 - tan20 du = | cscu . du 2 - 2 sinu . 2 2 = NIH (- In|cscu + cotul) - (- cos u) + C = - NIH In|csc 20 + cot 20| + cos 20 + C