Prove that: `("sin"(x+theta))/("sin"(x+phi))=cos(theta-phi)+cot(x+phi)sin(theta-phi)dot`

(sin theta-sin phi)^(2)+(cos theta-cos phi)^(2)=4sin^(2)(theta-phi)/(2)

prove that (cos3 theta+cos3 phi)/(2cos(theta+phi)-1)=(cos theta+cos phi)cos(theta+phi)-(sin theta+sin phi)sin(theta+phi)

Prove that (sin(theta+phi)-2sintheta+sin(theta-phi))/(cos(theta+phi)-2costheta+cos(theta-phi))=tantheta

Compute the following: {:[(sin(theta+phi), cos(theta+phi)),(sin(theta - phi),cos(theta-phi))] +[(sin(theta-phi), cos(theta-phi)),(sin(theta+phi), cos(theta+phi))]

If "sin" theta+"sin" phi=a and cos theta+cos phi=b find: (i) "sin"(theta+phi) (ii) cos(theta+phi) (iii) cos(theta-phi)

"cos"2theta."cos"2phi+"sin"^(2)(theta-phi)-"sin"^(2)(theta+phi) is equal to (i) "sin"2(theta+phi) (ii) "cos"2(theta+phi) (iii) "sin"2(theta-phi) (iv) "cos"2(theta-phi)

(sin ( theta -phi))/(sin theta sin phi) = cot phi - cot theta.

If sin theta+ sin phi= a and cos theta+ cos phi= b , find : sin (theta+ phi) .

If sin theta+ sin phi= a and cos theta+ cos phi= b , find : cos (theta- phi) .

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