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

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

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)-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

Prove that :2sin^(2)theta+4cos(theta+alpha)sin alpha sin theta+cos2(alpha+theta) is independent of theta.

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

Show that cos^(2)theta+cos^(2)theta(alpha+theta)-2cos alpha cos theta cos(alpha+theta) is independent of theta.

Factors of cos4theta-cos4varphi are- a. (costheta+cosvarphi) b. \ (costheta-cosvarphi) c. ("costheta"+"sin") d. (costheta-s invarphi)

Evaluate: int(2sin2varphi-cosvarphi)/(6-cos^2varphi-4\ sinvarphi)\ dvarphi