If `costheta=1/2\ a n d\ pi

If costheta=1/2 and pi< theta < (3pi)/2 , find the value of 4tan^2theta-3cos e c^2thetadot

If costheta=4/5a n d\ theta is acute, find the t a n2theta

If A=[costheta-sinthetasinthetacostheta] , then A^T+A=I_2 , if theta=npi,\ \ n in Z (b) theta=(2n+1)pi/2,\ \ n in Z (c) theta=2n\ pi+pi/3,\ \ n in Z (d) none of these

If m^2 + m'^2 + 2mm' costheta = 1 and n^2+n'^2+2n n'costheta=1 , (mn + m' n' + (m n' + m' n) costheta = 0 prove that m^2 + n^2 = cosec^2theta

The most general value for which tantheta=-1 and costheta=1/(sqrt(2)) is ( n in Z) (A) npi+(7pi)/4 (B) npi+(-1)^n(7pi)/4 (C) 2npi+(7pi)/4 (D) none of these

If cosectheta-sintheta=m a n d sectheta-costheta=n ,"eliminate"theta

If 1//x+x=2costheta , then prove that x^n+1//x^n=2cosnthetadot

The vector vec a\ a n d\ vec b satisfy the equation 2 vec a+ vec b= vec p\ and vec a+2 vec b= vec q ,\ w h e r e\ vec p= hat i+ hat j\ a n d\ vec q= hat i- vec jdot If theta is the angle between vec a\ a n d\ vec b"\ " , then a. costheta=4/5 b. sintheta=1/(sqrt(2)) c. costheta=\ -4/5 d. costheta=-3/5

For -pi/2 lt theta lt pi/2, (sintheta + sin 2theta)/(1+costheta + cos2theta) lies in the interval

(sin^3theta-cos^3theta)/(sintheta-costheta)-(costheta)/(sqrt(1+cot^2theta))-2tanthetacottheta=-1 if theta in (0,pi/2) (b) theta in (pi/2,pi) theta in (pi,(3pi)/2) (d) theta in ((3pi)/2,2pi)