Let `alpha,betaa n dgamma` be some angles in the first quadrant satisfying `tan(alpha+beta)=(15)/8a n dcos e cgamma=(17)/8,` then which of the following hold(s) good? (a) `alpha+beta+gamma=pi` (b)`cotalpha+cotbeta+cotgamma=cotalphacotbetacotgamma` (c)`tanalpha+tanbeta+tangamma=tanalphatanbetatangamma` (d)`tanalphatanbeta+tanbetatangamma+tangammatanalpha=1`

Which of the following identities, wherever defined, hold(s) good? (a)cotalpha-tanalpha=2cot2alpha (b)tan(45^0+alpha)-tan(45^0-alpha)=2cos e c2alpha (c)tan(45^0+alpha)+tan(45^0-alpha)=2sec2alpha (d)tanalpha+cotalpha=2tan2alpha

If (tan(alpha+beta-gamma))/("tan"(alpha-beta+gamma))=(tangamma)/(tanbeta),(beta!=gamma) then sin2alpha+sin2beta+sin2gamma= (a) 0 (b) 1 (c) 2 (d) 1/2

If alpha,beta,gamma are such that alpha+beta+gamma=2,""alpha^2+beta^2+gamma^2=6,""alpha^3+beta^3+gamma^3=8,t h e n""alpha^4+beta^4+gamma^4 is a. 18 b. 10 c. 15 d. 36

If alpha,beta are the roots of the quadratic equation a x^2+b x+c=0 , then which of the following expression will be the symmetric function of roots a. |log(alpha/beta)| b. alpha^2beta^5+beta^2alpha^5 c. t a n(alpha-beta) d. (log(1/alpha))^2+(logbeta)^2

In R^(3) , consider the planes P_(1):y=0 and P_(2),x+z=1. Let P_(3) be a plane, different from P_(1) and P_(2) which passes through the intersection of P_(1) and P_(2) , If the distance of the point (0,1,0) from P_(3) is 1 and the distance of a point (alpha,beta,gamma) from P_(3) is 2, then which of the following relation(s) is/are true? (a) 2alpha + beta + 2gamma +2 = 0 (b) 2alpha -beta + 2gamma +4=0 (c) 2alpha + beta - 2gamma- 10 =0 (d) 2alpha- beta+ 2gamma-8=0

A tower P Q stands at a point P within the triangular park A B C such that the sides a , ba n dc of the triangle subtend equal angles at P , the foot of the tower. if the tower subtends angles alpha,betaa n dgamma,a tA , Ba n dC respectively, then prove that a^2(cotbeta-cotgamma)+b^2(cotgamma-cotalpha)+a^2(cotalpha-cotbeta)=0

Let x,y,z in R^(+) and 2xy+3yz+4xz=18 . If alpha , beta and gamma be the values of x , y and z respectively, for which xyz attains its maximum value, then the value of 2alpha+beta+gamma= (a) 4 (b) 6 (c) 8 (d) 12

If alpha,beta,gamma,delta are the roots of the equation x^4-K x^3+K x^2+L x+m=0,w h e r eK ,L ,a n dM are real numbers, then the minimum value of alpha^2+beta^2+gamma^2+delta^2 is a. 0 b. -1 c. 1 d. 2

If alpha and beta are the rootsof he equations x^2-a x+b=0a n dA_n=alpha^n+beta^n , then which of the following is true? a) A_(n+1)=a A_n+b A_(n-1) b) A_(n+1)=b A_(n-1)+a A_n c) A_(n+1)=a A_n-b A_(n-1) d) A_(n+1)=b A_(n-1)-a A_n

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0a n dalpha^2,beta is the roots of quadratic equation x^2-q x+8=0 , then the value of rifr/8 is the arithmetic mean of p and q , is a. (83)/2 b. 83 c. (83)/8 d. (83)/4