If the determinant ∣ cos(θ+ϕ) sinθ −cosθ ​−sin(θ+ϕ) cosθ sinθ cos2ϕ sinϕ cosϕ ​∣ ​is positive is independent of `theta` `` is independent of `varphi` none of these

Prove that the determinant Delta =|{:(x,,sintheta,,cos theta),(-sin theta,,-x,,1),(cos theta,,1,,x):}| is independent of theta .

Prove that the determinant {:[( x, sin theta ,cos theta ),( -sin theta , -x , 1),( cos theta , 1,x) ]:} is independent of theta.

Show that cos^2theta+cos^2(alpha+theta)-2cosalphacostheta"cos"(alpha+theta) is independent of thetadot

If cosθ= 3/5 then the value of (sinθ−tanθ+1)/2tan^2θ ​

Let S_(1) be the set of all those solution of the equation (1+a) cos theta cos(2 theta-b)=(1+a cos 2 theta) cos (theta -b) which are independent of a and b and S_(2) be the set of all such solutions which are dependent on a and b. Then The set S_(1) and S_(2) are

Let S_(1) be the set of all those solution of the equation (1+a) cos theta cos(2 theta-b)=(1+a cos 2 theta) cos (theta -b) which are independent of a and b and S_(2) be the set of all such solutions which are dependent on a and b. Then Condition that should be imposed on a and b such that S_(2) in non empty is

Find the derivatives of the following functions with respect to corresponding independent variables: y = tan(Theta)(sin(Theta) + cos(Theta))

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

The expression cos 3 theta + sin 3 theta + (2 sin 2 theta-3) (sin theta- cos theta) is positive for all theta in