If `tanalpha=1/7,sin beta=1/(sqrt(10)),` prove that`alpha+2beta=pi/4`

If tanalpha=1/3,tanbeta=1/7 ,show that 2alpha +beta=pi/4

If tan(alpha-beta)=(sin2beta,)/(3-cos2beta) then (a) tanalpha=2tanbeta (b) tanbeta=2tanalpha (c) 2tanalpha=3tanbeta (d) 3tanalpha=2tanbeta

If sin alpha sin beta-cosalphacosbeta+1=0, then prove that 1+cotalphatanbeta=0

If (cos^(4)alpha)/(cos^(2) beta) + (sin^(4)alpha)/(sin^(2)beta) = 1, prove that sin^(4)alpha + sin^(4) beta = 2 sin^(2) alpha sin^(2) beta

If cosalpha+cosbeta+cosgamma=0a n da l sosinalpha+sinbeta+singamma=0, then prove that cos2alpha+cos2beta+cos2gamma =sin2alpha+sin2beta+sin2gamma=0 sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma) cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

If (cos^(4)alpha)/(cos^(2) beta) + (sin^(4)alpha)/(sin^(2)beta) = 1, prove that (cos^(4)beta)/(cos^(2) alpha) + (sin^(4)beta)/(sin^(2)alpha)= 1

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

Let alpha , beta be such pi lt alpha- beta lt 3 pi if sin alpha + sin beta = (-21)/(65) , and cos alpha Cos beta = (-27)/(65) then the value of cos ( alpha - beta)/(2) is

If 2alpha= -1-isqrt(3)" and"2beta= -1+isqrt(3) , then 5alpha^(4)+5beta^(4)+7alpha^(-1)beta^(-1) is equal to

The points A(0,0),B(cosalpha,sinalpha) and C(cosbeta,sinbeta) are the vertices of a right-angled triangle if (a) sin((alpha-beta)/2)=1/(sqrt(2)) (b) cos((alpha-beta)/2)=-1/(sqrt(2)) (c) cos((alpha-beta)/2)=1/(sqrt(2)) (d) sin((alpha-beta)/2)=-1/(sqrt(2))