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

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

If cos alpha+cos beta=1/3 and sin alpha+sin beta=1/4 ,show that tan((alpha+beta)/2)=3/4

If cos^(2)alpha-sin^(2)alpha=tan^(2)beta , then prove thta tan^(2)alpha=cos^(2)beta-sin^(2)beta .

If cot alpha cot beta=2 , show that (cos (alpha+beta))/(cos (alpha-beta))=(1)/(3)

Evaluate |[cos alpha cos beta, cos alpha sin beta, -sin alpha],[ -sin beta, cos beta, 0],[ sin alpha cos beta, sin alpha sin beta, cos alpha]|

If cosalpha+cosbeta=0=sinalpha+sinbeta,cos2alpha+cos2beta is equal to a) -2sin(alpha+beta) b) 2cos(alpha+beta) c) 2sin(alpha-beta) d) -2cos(alpha+beta)

If A=[(cos^2alpha,cosalphasinalpha),(cosalphasinalpha,sin^2alpha)] and B=[(cos^2beta,cosbetasinbeta),(cosbetasinbeta,sin^2beta)] . Show that AB=[(cosalphacosbetacos(alpha-beta),sinbetacosalphacos(alpha-beta)),(cosbetasinalphacos(alpha-beta),sinbetasinalphacos(alpha-beta))]

The foci of the hyperbola (x ^(2))/( cos ^(2) alpha ) -( y ^(2))/( sin ^(2) alpha ) = 1 are