Home
Class 11
MATHS
Let alpha, beta, gamma satisfy 0 lt alph...

Let `alpha, beta, gamma` satisfy `0 lt alpha lt beta lt gamma lt 2pi` and `cos(x+alpha) + cos(x + beta) + cos(x + gamma) =0` for all `x in R` observe the following statements.
Statements-I: `gamma - alpha =(2pi)/3`
Statement-2: `cos alpha + cos beta + cos gamma=0` and `sin alpha + sin beta + sin gamma=0`

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True, Statement-2 NOT a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False

D

Statement -1 is False, Statement-2 is True.

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Similar Questions

Explore conceptually related problems

If cos alpha + cos beta + cos gamma =3 , " then " sin alpha + sin beta + sin gamma =

cos alpha + cos beta + cos gamma + cos ( alpha + beta + gamma ) =

Let alpha,beta and gamma be such that 0 lt alpha lt beta lt gamma lt 2pi for any x in R if cos (x+alpha)+cos(x + beta)+cos(x+gamma)=0 then tan(gamma-alpha) =

If alpha,beta, gamma are any three angles , then cos alpha + cos beta - cos gamma - cos (alpha+beta+gamma)=

If alpha + beta + gamma = 2 theta , " then " cos theta + cos ( theta - alpha ) + cos (theta - beta ) + cos ( theta - gamma ) =

If cos alpha+2cos beta+3cos gamma=sinalpha+2sinbeta+3singamma=0 then sin 3alpha+8sin3 beta+27sin 3gamma=

If alpha+beta=gamma. then cos^(2)alpha+cos^(2)beta+cos^(2)gamma-2 cos alpha cos beta cos gamma=

Given alpha+beta+gamma=pi then sin^2alpha+sin^2beta-sin^2gamma is equal to……

cos alpha * sin (beta - gamma ) + cos beta * sin ( gamma - alpha ) + cos gamma * sin ( alpha - beta )=