(i) `cos3x=cos2x`
(ii) `cos5x=sin3x`
(iii) `cosmx=sinnx`

Find the general solution for each of the following equations : (i) cos4x=cos2x (ii) cos3x=sin2x (iii) sin3x+cos2x=0 (iv) sinmx+sinnx=0

cos3x-cos2x=sin3x

(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

Find the maximum and the minimum values of the following function over R. (i) sin^(2) X (ii) 7 cos x -24 sin x + 5 (iii) 3 sin x-4 cos x (iv) 3 cos (4x -5) + 4 (v ) (sin x+ cos x) (vi) 5 sin x + 12 cosx + 13 (vii) (3 sin^(2) x+ 4) (ix) 5 sin x + 12 cos x -13

Some examples Type: 1 (1) (sin5A-sin3A)/(cos5A+cos3A)=tan A(2)(sin3x+sin x)sin x+(cos3x-cos x)cos x=0 (3) Prove that cot4x(sin5x+sin3x)=cot x(sin5x-sin3x)

sin x+sin2x+sin3x=cos x+cos2x+cos3x if (i)cos x=-(1)/(2)( ii) sin2x=cos2x (iii) x=n(pi)/(2)+(pi)/(8)( iv )x=2n pi+(2 pi)/(3)

(sin5x+sin3x)/(cos5x+cos3x)=tan4x

int (sin ^ (2) x cos ^ (2) x) / ((sin ^ (5) x + cos ^ (3) x sin ^ (2) x + sin ^ (3) x cos ^ (2) x + cos ^ (5) x) ^ (2)) dx