If determinant `|"cos"(theta+varphi)-"sin"(theta+varphi)cos2varphis inthetacosthetas invarphi-costhetas inthetacosvarphi|` is a. positive b. independent of `q` c. independent of `varphi` 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 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 =|s inthetacosvarphisinthetas invarphicosthetacosthetacosvarphicosthetas invarphi-s intheta-s inthetas invarphis inthetacosvarphi0| then is independent of theta is independent of varphi "Delta" is a constant ((d"Delta")/(dtheta)])_(theta=pi//2)=0

If =|s inthetacosvarphisinthetas invarphicosthetacosthetacosvarphicosthetas invarphi-s intheta-s inthetas invarphis inthetacosvarphi0| then is independent of theta is independent of varphi "Delta" is a constant ((d"Delta")/(dtheta)])_(theta=pi//2)=0

If =|s inthetacosvarphisinthetas invarphicosthetacosthetacosvarphicosthetas invarphi-s intheta-s inthetas invarphis inthetacosvarphi0| then is independent of theta is independent of varphi "Delta" is a constant ((d"Delta")/(dtheta)])_(theta=pi//2)=0

Prove that: (sin(theta+varphi)-2sintheta+"sin"(theta-varphi))/(cos(theta+varphi)-2costheta+"cos"(theta-varphi))=t a ntheta

Prove that: (sin(theta+varphi)-2sin theta+sin(theta-varphi))/(cos(theta+varphi)-2cos theta+cos(theta-varphi))=tan theta

(tan(theta+varphi)+tan(theta-varphi))/(1-tan(theta+varphi)tan(theta-varphi))=tan2 theta

If 3tanthetatanvarphi=1 , then prove that 2cos(theta+varphi)=cos(theta-varphi) .

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