If `A+B = alpha` and `sin A =k sin B`, show that :
`tanA= (k sin alpha)/(1+k cos alpha)`.

If tan beta= (Q sin alpha)/(P+Q cos alpha) , prove that : tan (alpha-beta)= (P sin alpha)/(Q+P cos alpha) .

If theta+phi= alpha and tan theta=k tan phi , prove that : sin alpha=(k+1)/(k-1) sin (theta-phi) .

If sin theta= n sin(theta+2 alpha) , show that : tan(theta+ alpha)=(1+n)/(1-n) tan alpha .

Evalute int (sin(x-alpha))/(sin(x+alpha))

If alpha = 112^(@) 30' , find the value of sin alpha and cos alpha

One side of a square makes an angle alpha with x axis and one vertex of the square is at origin. Prove that the equations of its diagonals are x(sin alpha+ cos alpha) =y (cosalpha-sinalpha) or x(cos alpha-sin alpha) + y (sin alpha + cos alpha) = a , where a is the length of the side of the square.

Using vectors, prove that sin (alpha+beta)=sin alpha cos beta+ cos alpha sin beta .

lf cos^2 alpha -sin^2 alpha = tan^2 beta , then show that tan^2 alpha = cos^2 beta-sin^2 beta .