If `(x)/(tan(theta+alpha))=(y)/(tan(theta+beta))=(z)/(tan(theta+gamma))`. Then show that `sum(x+y)/(x-y)sin^(2)(a-beta)=0`.

If ("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma))/c then prove (a+b)/(a-b)sin^2(alpha-beta)+(b+c)/(b-c)sin^2(beta-gamma)+(c+a)/(c-a)sin^2(gamma-alpha)=0

If ("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma))/c then (a+b)/(a-b)sin^2(alpha-beta)+(b+c)/(b-c)sin^2(beta-gamma)+(c+a)/(c-a)sin^2(gamma-alpha)=0

What is the equation of the plane which passes through the z-axis and is perpendicular to the line (x-a)/(cos theta) = (y+2)/(sin theta) = (z-3)/0 ? (A) x+y tan theta=0 (B) y+x tan theta=0 (C) x cos theta-y sin theta=0 (D) x sin theta-y cos theta=0

If alpha+beta=theta and (tan alpha)/(tan beta) = x/y , prove that sin (alpha-beta) = (x-y)/(x+y) sin theta

If tan theta+sin theta=alpha and tan theta-sin theta=beta , show that alpha^(2)-beta^(2)=4sqrt(alphabeta)." "(theta in" II or III quad.")

If tan 3 theta + tan theta =2 tan 2 theta , then theta is equal to (n in Z)

If cos theta=cos alpha cos beta then tan((theta+alpha)/2) tan((theta-alpha)/2)= (i) tan^2(alpha/2) (ii) tan^2(beta/2) (iii) tan^2(theta/2) (iv) cot^2(beta/2)

If 2(cos ( alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)+3=0 , prove that (d alpha)/(sin ( beta+theta)sin(gamma+theta))+(d beta)/(sin(alpha+beta)sin(beta+theta))+(d gamma)/(sin(alpha+theta)sin(beta+theta))=0 , where, 'theta' is any real angle such that alpha+theta, beta+theta, gamma+theta are not the multiple of pi .

The equation of the bisectors of the angles between the two intersecting lines (x-3)/(cos theta ) = (y+5)/(sin theta) and (x-3)/(cos theta) = (y+5)/(sin theta) are (x-3)/(cos alpha) = (y+5)/(sin alpha) and (x-3)/beta = (y+5)/gamma , then

If a chord joining P(a sec theta, a tan theta), Q(a sec alpha, a tan alpha) on the hyperbola x^(2)-y^(2) =a^(2) is the normal at P, then tan alpha is (a) tan theta (4 sec^(2) theta+1) (b) tan theta (4 sec^(2) theta -1) (c) tan theta (2 sec^(2) theta -1) (d) tan theta (1-2 sec^(2) theta)