`(costheta-sintheta)/(costheta+sintheta)=sec2theta-tan2theta`

Prove that (1+costheta+sintheta)/(1-costheta+sintheta)=cot(theta/2)

If cos(2theta)=0" then "|{:(0,costheta,sintheta),(costheta,sintheta,0),(sintheta,0,costheta):}|^2="............"

Prove that: (i) (costheta)/(1-sintheta)=(1+sintheta)/(costheta) (ii) (1+costheta-sin^(2)theta)/(sintheta+sinthetacostheta)=cottheta (iii) 1+(tan^(2)theta)/(1+sectheta)=sectheta

If (costheta+sintheta)/(costheta-sintheta)=8 then the value of cot theta is equal to:

Evalute : |{:(cos^2 theta,costhetasintheta,-sintheta),(costhetasintheta,sin^2theta,costheta),(sintheta,-costheta,0):}|

The value of f(pi/6) where f(theta)=|{:(cos^2theta,costhetasintheta,-sintheta),(costhetasintheta,sin^2theta,costheta),(sintheta,-costheta,0):}|

The value of f(pi/6) where f(theta)=|{:(cos^2theta,costhetasintheta,-sintheta),(costhetasintheta,sin^2theta,costheta),(sintheta,-costheta,0):}|

If f(theta)=|{:(cos^2theta,costhetasintheta,-sintheta),(costhetasintheta,sin^2theta,costheta),(sintheta,-costheta," "0):}| , then find the value of f((pi)/6) .