The value of the determinant `|(cos(theta+phi),-sin(theta+phi),cos2phi),(sin theta,cos theta, sin phi), (-cos theta , sin theta ,cos phi)|` is

if determinant |{:( cos (theta + phi),,-sin (theta+phi),,cos 2phi),(sin theta,,cos theta,,sin phi),(-cos theta,,sintheta,,cos phi):}| is

if determinant |{:( cos (theta + phi),,-sin (theta+phi),,cos 2phi),(sin theta,,cos theta,,sin phi),(-cos theta,,sintheta,,cos phi):}| is

if determinant |{:( cos (theta + phi),,-sin (theta+phi),,cos 2phi),(sin theta,,cos theta,,sin phi),(-cos theta,,sintheta,,cos phi):}| is

The determinant |(cos(theta+phi),-sin(theta+phi),cos2phi),(sintheta,costheta,sinphi),(-costheta,sintheta,cosphi)| is

If determinant |[cos(theta+phi),-sin(theta+phi),cos2phi],[sin theta,costheta, sinphi],[-costheta,sintheta,cosphi]| is a. positive b. independent of theta c. independent of phi d. none of these

If determinant |cos(theta+phi) sin(theta+phi)cos2phi sin thetacostheta sinphi costheta sintheta cosphi | is a. positive b. independent of theta c. independent of phi d. none of these

If theta, phi epsilon R , then the determinant Delta=|(cos theta, - sin theta, 1),(sin theta, cos theta, 1),(cos(theta+phi),-sin(theta+phi),0)| lies in the interval

The value of ((sin theta + sin phi)/(cos theta + cos phi)+ (cos theta - cos phi)/(sin theta - sin phi)) is :