" (i) "sin(2x+3)" (i) "

Differentiate the following with respect to x. (i) sin 2x (ii) cos 3x (iii) tan 4x (iv) sin^3x (v) x^2//tan x

Integrate with respect to x: i) sin^(2)x , ii) cos^(3)x , iii) sin2xcos3x , iv) 1/(sqrt(x+3)-sqrt(x+2))

Integrate with respect to x: i) sin^(2)x , ii) cos^(3)x , iii) sin2xcos3x , iv) 1/(sqrt(x+3)-sqrt(x+2))

If 2 sin x = sqrt(3) , evaluate (i) 4 sin^(3)x - 3 sin x (ii) 3 cos x - 4 cos^(3)x

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 x^(2)(sin^(2)x^(3))dx

Sketch the graphs of the following function: (i) y=2 sin x (ii) y=3 "sin"(x+1) (iii) y="sin"(x)/(2)

(i) int " x sec"^(2) " 2x dx "" "(ii) int " x sin"^(3) " x dx "

(i) int " x sec"^(2) " 2x dx "" "(ii) int " x sin"^(3) " x dx "

sin^(2) x+2sin x cos x-3cos^(2) x = 0 if (i) tan x = 3 (ii) tan x = -1 (iii) x = n pi+(pi)/(4) , n in I (iv) x = n pi+tan^(-1) (3), n in I