Let `f_n(theta)=(cos(theta/2)+cos2theta+cos((7theta)/2)+....+cos(3n-2)(theta/2))/(sin(theta/2)+sin2theta+sin((7theta)/2)+....+sin(3n-2)(theta/2))` then (a)`f_3((3pi)/(16))=sqrt(2)-1` (b) `f_5(pi/(28))=sqrt(2)+1` (c)`f_7(pi/(60))=(2+sqrt(3))` (d) none of these

Let f_n(theta)=(cos theta/2+cos 2theta + cos (7theta)/2+...+cos (3n-2) (theta/2))/(sin theta/2+sin 2theta + sin (7theta)/2+....+ sin (3n-2)(theta/2)) then f_3((3pi)/16)

Let f_(n)(theta)=(cos((theta)/(2))+cos2 theta+cos((7 theta)/(2))+...+cos(3n-2)((theta)/(2)))/(sin((theta)/(2))+sin2 theta+sin((7 theta)/(2))+...+sin(3n-2)((theta)/(2))) then (a)f_(3)((3 pi)/(16))=sqrt(2)-1(b)f_(5)((pi)/(28))=sqrt(2)+1(c)f_(7)((pi)/(60))=(2+sqrt(3))(d) none of these

Let f_(n)(theta)=((cos theta)/(2)+cos2 theta+(cos(7 theta))/(2)+...+cos(3n-2)((theta)/(2 ))/((sin theta)/(2)+sin2 theta+(sin(7 theta))/(2)+...+sin(3n-2)((theta)/(2))) then f_ (3)((3 pi)/(16))

cos3theta + cos2theta = sin ((3theta)/2)+ sin (theta/2), 0 le theta le 2pi

(cos3 theta+2cos5 theta+cos7 theta)/(cos theta+2cos3 theta+cos5 theta)=cos2 theta-sin2 theta tan3 theta

Range of f(theta)=cos^2theta(cos^2theta+1)+3sin^2theta is

If f(theta)=|(cos^(2) theta, cos theta sin theta, -sin theta),(cos theta sin theta, sin^(2) theta, cos theta),(sin theta, -cos theta, 0)| then f((pi)/12)=

int_(pi//4) ^(pi//2) (cos theta)/((cos (theta/2) + sin (theta/2))^(3))d theta=

|(sin theta, cos theta, sin2theta),(sin(theta+(2pi)/(3)),cos(theta+(2pi)/(3)),sin(2theta+(4pi)/(3))),(sin(theta-(2pi)/(3)),cos(theta-(2pi)/(3)),sin(2theta-(4pi)/(3)))|=