If `(3pi)/4 lttheta<2pi` and `cos theta=1/4` find `tan (theta/2)`

For -(pi)/(2)lttheta(pi)/(2),(sintheta+sin2theta)/(1+costheta+cos2theta) lies in the interval

tan ((pi)/(4)+theta) tan ((3pi)/( 4) + theta) is equal to

If tan((pi)/(4)+theta)+tan((pi)/(4)-theta)=a then tan^(3)((pi)/(4)+theta)+tan^(3)((pi)/(4)-theta)=

If (pi)/(2) and (pi)/(4) are the arguments of z_ (1) and bar (z_ (2)) respectively, then Arg ((z_ (1))/(z_ (2)) ) = (i) 3 (pi)/(4) (ii) (pi)/(4) (iii) pi (iv) (pi)/(3)

If tan(picostheta)=cot(pisintheta),0lt thetalt(3pi)/(4), then sin(theta+(pi)/(4)) equals

f(x)=min(sin x,cos x),x in(-pi,pi) the values of x where f(x) is non differentiable,is the set A. Then A is subset of (A) {(-3 pi)/(4),(-pi)/(4),(3 pi)/(4)}(B){(-pi)/(4),(pi)/(4),(3 pi)/(3)}(C){(-3 pi)/(4),(3 pi)/(4)}(D){(-3 pi)/(4),(pi)/(4),(pi)/(4),(3 pi)/(4)}

If 4cos^(2)theta=3 then theta =---- 1) (pi)/(6),(5 pi)/(6) 2) (pi)/(4),(3 pi)/(4) 3) (pi)/(3),(2 pi)/(3) 4) +-(pi)/(2)

If cos(sinx)=0, then x lies in (a) (pi/4,pi/2)uu(pi/2,\ pi) (b) (-pi/4,\ 0) (c) (pi,(3pi)/2) (d) null set

Show that :(i) sin^(-1) [ sin. (3pi)/4] != (3pi)/4 (ii) tan^(-1) [ tan. (5pi)/6] != (5pi)/6 . What is its value ?