`If x cos alpha + y sin alpha=x cos beta+y sin beta,"show that",y=x "tan"(alpha+beta)/2`

If x cos alpha + y sin alpha = x cos beta + y sin beta "then" "tan" (alpha + beta)/2=

If x cos alpha + y sin alpha = x cos beta + y sin beta "then" (2(1-cos (alpha - beta)))/(cos beta - cos alpha)^(2)=

If x cos alpha + y sin alpha = x cos beta + y sin beta "then" (sin alpha - cos alpha - sin beta + cos beta)/(sin alpha + cos alpha - sin beta - cos beta)=

If sin alpha sin beta - cos alpha cos beta + 1 = 0,"show that", sin (alpha + beta) = 0, "hence deduce that," 1 + cot alpha tan beta = 0.

If cos alpha+ cos beta= a sin alpha+ sin beta=b , then show that "tan" (alpha)/(2)+"tan" (beta)/(2)= (4b)/(a^(2)+b^(2)+2a)

If tan beta = (n sin alpha cos alpha)/(1-n sin^(2) alpha), "show that", tan (alpha - beta) = (1 - n) tan alpha.

If cos alpha = k cos beta , "show that", "tan" ( alpha+beta)/2 = ( 1-k)/(1+k)"cot" (alpha-beta)/2

If sin alpha = sin beta and cos alpha = cos beta then-

Under rotation of axes through theta , x cosalpha + ysinalpha=P changes to Xcos beta + Y sin beta=P then . (a) cos beta = cos (alpha - theta) (b) cos alpha= cos( beta - theta) (c) sin beta = sin (alpha - theta) (d) sin alpha = sin ( beta - theta)

If sin 2 alpha = 4 sin 2 beta, "show that", 5tan ( alpha -beta) = 3 tan ( alpha +beta)