" 4."sin x sin(cos x)quad " 5."sin(ax+b)

The number of distinct real roots of the equation, |(cos x, sin x , sin x ),(sin x , cos x , sin x),(sinx , sin x , cos x )|=0 in the interval [-pi/4,pi/4] is :

2 [ sin x - cos x ]^(4) + 6 [ sin x + cos x ]^(2) + 5 [ sin^(6)x + cos^(6) x ] = ? (a)6 (b)4 (c)3 (d)13

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

If a sin^(3)x+b cos^(3)x= sin x cos x and a sin x= b cos x then a^(2)+b^(2)=

sin4x=4sin x cos^(3)x-4cos x sin^(3)x

What is the value of [(sin7x- sin5x)/ (cos 7x + cos 5x)]- [(cos 6x-cos 4x)/ (sin 6x + sin 4x)] ? [(sin7x- sin5x)/ (cos 7x + cos 5x)]- [(cos 6x-cos 4x)/ (sin 6x + sin 4x)] का मान क्या है?

5. sin(ax+b)cos(ax+b)

Prove that: sin x + sin 3x + sin 5x + sin 7x= 4 cos x cos 2x sin 4x