If `p(x)=sinx(sin^3x+3)+cosx(cos^3x+4)+(1/2)sin^2 2x+5,` then find the range of `p(x)dot`

(sin x + sin 3x )/( cos x + cos 3x )= tan 2x

Find the range of f(x)=1/(4cosx-3)dot

(sin 5x + sin 3x )/( cos 5x + cos 3x ) = tan 4x

If x=(sin^3P)/cos^2P,y=cos^3P/sin^2P" and " sinP+cosP=1/2 then find the value of x + y.

(3 + 4 cos x)/( sin^(2) x )

Find the range of f(x)=sin^2x-3sinx+2

Find the range of f(x)=sin^2x-sinx+1.

" Let " =|{:(cos x,,sin x,,cosx),( cos 2x,,sin 2x,,2cos 2x),(cos 3x,,sin 3x,,3cos 3x):}| then find the values of f(0) and f' (pi//2) .

(sin x - sin 3x)/( sin ^(2) x - cos ^(2) x) = 2 sin x