Home
Class 12
MATHS
Let alpha,betaa n dgamma satisfy 0<alpha...

Let `alpha,betaa n dgamma` satisfy `0

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the equation given: \[ \cos(x + \alpha) + \cos(x + \beta) + \cos(x + \gamma) = 0 \] for all \( x \in \mathbb{R} \). ...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Solved example|15 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Concept App. 3.1|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

If [alphabetagamma-alpha] is to be square root of two-rowed unit matrix, then alpha,betaa n dgamma should satisfy the relation. 1-alpha^2+betagamma=0 b. alpha^2+betagamma=0 c. 1+alpha^2+betagamma=0 d. 1-alpha^2-betagamma=0

If alpha,betaa n dgamma are roots of 2x^3+x^2-7=0 , then find the value of sum(alpha/beta+beta/alpha) .

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

If each of alpha, betaa n dgamma is a positive acute angle such that sin(alpha+beta-gamma) =1/2 , cos(beta+gamma-alpha)=1/2 and tan(gamma+alpha-beta)=1, find the values of alpha,betaa n dgammadot

The side of a triangle inscribed in a given circle subtends angles alpha,betaa n dgamma at the centre. The minimum value of the arithmetic mean of cos(alpha+pi/2),cos(beta+pi/2) , and cos(gamma+pi/2) is equal to ____

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

vec u , vec v and vec w are three non-coplanar unit vecrtors and alpha,beta and gamma are the angles between vec u and vec v , vec v and vec w ,a n d vec w and vec u , respectively, and vec x , vec y and vec z are unit vectors along the bisectors of the angles alpha,betaa n dgamma , respectively. Prove that [ vecx xx vec y vec yxx vec z vec zxx vec x]=1/(16)[ vec u vec v vec w]^2sec^2(alpha/2)sec^2(beta/2)sec^2(gamma/2) .

If [[alpha, beta], [gamma, -alpha]] is to be square root of two-rowed unit matrix, then alpha,beta and gamma should satisfy the relation. a. 1-alpha^2+betagamma=0 b. alpha^2+betagamma=0 c. 1+alpha^2+betagamma=0 d. 1-alpha^2-betagamma=0

If alpha,betaa n dgamma are the roots of x^3+8=0 then find the equation whose roots are alpha^2,beta^2a n dgamma^2 .

A line makes angles alpha,betaa n dgamma with the coordinate axes. If alpha+beta=90^0, then find gammadot