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`

Match the column Column I (Function), Column II (Period) p. f(x)=sin^3x+cos^4x , a. pi/2 q. f(x)=cos^4x+sin^4x , b. pi r. f(x)=sin^3x+cos^3x , c. 2pi s. f(x)=cos^4x-sin^4x ,

{.} denotes the fractional part function and [.] denotes the greatest integer function: Column I: Function, Column II: Period f(x)=e^cos^4pix+x-[x]+cos^(2pix) , p. 1//3 f(x)=cos2pi{2x}+sin2pi{2x} , q. 1//4 f(x)=sin3pi{x}+tanpi[x] , r. 1//2 f(x)=3x-[3x+a]-b ,w h e r ea , b , in R^+ , s. 1

Find the period of the following function (i) f(x) =|sinx|+|cosx| (ii) f(x)=cos(cosx)+cos(sinx) (iii) f(x)= (|sinx+cosx|)/(|sinx|+|cosx|)

The function f(x) is defined on the interval [0.1] Then match the following columns Column I: Function, Column II: Domain f(tanx) , p. [2npi-ddotpi/2,2npi+pi/2],n in Z f(sinx) , q. [2npi,2npi+pi/6]uu[2npi+(5pi)/6,(2n+1)pi],n in Z f(cosx) , r. [2npi,(2n+1)pi],n in Z f(2sinx) , s. [npi,npi+pi/4],n in Z

Solve |sinx +cos x |=|sinx|+|cosx|, x in [0,2pi] .

Column I: Function, Column II: Type of function f(x)="{"sgnx")"^(sgn)}; x!=0,n is an odd integer, p. odd function f(x)=x/(e^x-1)+x/2+1 , q. even function f(x)={0,ifxi sr a t ion a l1,ifxi si r r a t ion a l , r. neither odd nor even function. f(x)=max{tanx ,cotx} , s. periodic

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

Prove that: (sinx)/(cos3x)+(sin3x)/(cos9x)+(sin9x)/(cos27 x)=(1/2)(tan27 x-tanx)

f(x)=tanx" at "x=pi/2