" Qéu-u "2i" se inai : "(1)/(sin x cos^(3)x)

Evaluate: (i) int(1)/(sin^(3)x cos^(5)x)dx (ii) int(1)/(sin^(3)x cos x)dx

Prove that: (i) sin 3x+"sin" 2x-"sin" x = 4 sin x cos((x)/(2))cos((3x)/(2)) (ii) ("sin" 3x+"sin" x)"sin" x+(cos 3x-cos x)cos x=0.

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx

3. (sin x+cos x)(1-sin x cos x)=sin^(3)x+cos^(3)x

(i) if sin x= (1)/(3) find the value of sin 3x (ii) if cos x= (1)/(2) , find the value of cos 3x

(i) int sin^2x cos^3x dx (ii) int sin^3 x cos^2 x dx (iii) int sin^3 x cos^3 x dx

If 0

Evaluate: ( i int(sin^(3)x-cos^(3)x)/(sin^(2)x cos^(2)x)dx (ii) int(5cos^(3)x+6sin^(3)x)/(2sin^(2)x cos^(2)x)dx