If `2|sin2alpha|=|tanbeta+cotbeta|,alpha,beta in (pi/2,pi),` then the value of `alpha+beta` is (a)`(3pi)/4` (b) `pi` (c) `(3pi)/2` (d) `(5pi)/4`

If 2 sin 2alpha=tan beta,alpha,beta, in((pi)/(2),pi) , then the value of alpha+beta is

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

Let f(theta)=cottheta/(1+cottheta) and alpha+beta=(5pi)/4 then the value f(alpha)f (beta) is

If sin^4alpha+cos^4beta+2=4sinalphacosbeta,0lt=alpha,betalt=pi/2 then find the value of (sinalpha+cosbeta)dot

Given both thetaa n dphi are acute angles and sintheta=1/2,cosvarphi=1/3, then the value of theta+varphi belongs to (a) (pi/3,pi/2] (b) (pi/2,(2pi)/3] (c) ((2pi)/3,(5pi)/6] (d) ((5pi)/6,pi]

If (costheta+cos2theta)^3=cos^3theta+cos^3 2theta, then the least positive value of theta is equal to pi/6 (b) pi/4 (c) pi/3 (d) pi/2

If sqrt(5-12 i)+sqrt(-5-12 i)=z , then principal value of a rgz can be pi/4 b. pi/4 c. (3pi)/4 d. -(3pi)/4

lf the eccentricity of the hyperbola x^2-y^2(sec)alpha=5 is sqrt3 times the eccentricity of the ellipse x^2(sec)^2alpha+y^2=25, then a value of alpha is : (a) pi/6 (b) pi/4 (c) pi/3 (d) pi/2

If (1+tanalpha)(1+tan4alpha)=2,alpha in (0,pi/(16)), then alpha is equal to (a) pi/(20) (b) pi/(30) (c) pi/(40) (d) pi/(60)

If sin^(4)alpha+cos^(4)beta+2=4 sin alpha cos beta, 0 le alpha, (pi)/(2) , then (sin alpha+cos beta) is equal to