`f(x)=sin^2x+cos^4x+2` and `g(x)=cos(cosx)+cos(sinx)` Also let period f(x) and g(x) be `T_1` and `T_2` respectively then

Show that (sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x) = tan 2x

If f(x)=sinx+cosx and g(x)=x^2-1 , then g(f (x)) is invertible in the domain .

If f(x)=sinx+cosx and g(x)=x^2-1 , then g(f (x)) is invertible in the domain .

Column I: Function, Column II: Period f(x)="cos"(|sinx|-|cosx|) , p. pi f(x)="cos"(tanx+cotx)cos(tanx-cotx) , q. pi/2 f(x)=sin^(-1)(sinx)+e^(tanx) , r. 4/pi f(x)=sin^3xsin3x , s. 2pi

f'(sin^(2)x)lt f'(cos^(2)x) for x in

Evaluate int sin x cos x cos2x cos 4x cos 8x dx

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

(cos 4x +cos 3x + cos 2x )/( sin 4x + sin 3x + sin 2x)= cot 3x

Prove that (sin 4x + sin 2x)/(cos 4x + cos 2x) = tan 3x .

(cosx)/((1-sinx)(2-sinx)) [Hint : Put sin x = t]