" 4.(i) "sin^(2)x

Prove that: (i) "sin"^(2)6x-"sin"^(2)4x="sin" 2x sin 10x (ii) cos^(2)2x-cos^(2)6x="sin" 4x sin 8x .

Find the general solution of each of the equations : (i) 4sin^(2)x=1 (ii) 2 cos^(2)x=1 (iii) cot^(2)x=3

Solve the following trigonometric equations, (i) 4 cos^(2)x+6"sin"^(2)x=5 (ii) 7 "sin"^(2)x+3 cos^(2)x=4 .

" 4.(i) "int(sin x)/(1-sin^(2)x)dx

Solve (i)7cos^(2)theta+3sin^(2)theta=4(ii)2sin^(2)x+sin^(2)2x=2( iii) 4sin x sin2x sin4x=sin3x

Show that (i) sin ^(2) 6 x-sin ^(2) dot(4) x=sin 2 x sin 10 x (ii) cos ^(2) 2 x-cos ^(2) 6 x=sin 4 x sin 8 x

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

The values of x in (0, pi) satisfying the equation. |{:(1+"sin"^(2)x, "sin"^(2)x, "sin"^(2)x), ("cos"^(2)x, 1+"cos"^(2)x, "cos"^(2)x), (4"sin" 2x, 4"sin"2x, 1+4"sin" 2x):}| = 0 , are

The values of x in (0, pi) satisfying the equation. |{:(1+"sin"^(2)x, "sin"^(2)x, "sin"^(2)x), ("cos"^(2)x, 1+"cos"^(2)x, "cos"^(2)x), (4"sin" 2x, 4"sin"2x, 1+4"sin" 2x):}| = 0 , are

(i) int e^(2x) ((1+sin2x)/(1+cos2x)) dx (ii) int e^(2x) ((sin4x-2)/(1-cos4x))