If alpha,beta,gamma, in (0,pi/2) , then ...

If `alpha,beta,gamma, in (0,pi/2)` , then prove that `(s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1`

`lt1`

`gt1`

`=1`

`=-1`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

TRIGONOMETRIC RATIOS AND IDENTITIES
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos
TRIGONOMETRIC RATIOS AND IDENTITIES
OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos
TRIGONOMETRIC EQUATIONS AND INEQUATIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

If alpha+beta+gamma=pi , prove that : cos^2 alpha + cos^2 beta + cos^2 gamma+2cosalpha cosbeta cosgamma=1 .

Given alpha+beta-gamma=pi, prove that sin^2alpha+sin^2beta-sin^2gamma=2sinalphasinbetacosgammadot

If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamma=0, then prove that cos2alpha+cos2beta+cos2gamma =sin2alpha+sin2beta+sin2gamma=0 sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma) cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

Determine the values of alpha ,beta , gamma when [{:( 0, 2beta, gamma),( alpha ,beta, -gamma),( alpha ,-beta, gamma):}] is orthogonal.

If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 , prove that cosalpha+cosbeta+cosgamma=sinalpha+sinbeta+singamma=0

Determine the values of alpha, beta, gamma when [{:(0,2sinbeta,tan gamma),(cos alpha, sin beta,-tan gamma),(cos alpha, -sin beta, tan gamma):}] is orthogonal.

If alpha, beta, gamma in [0,2pi] , then the sum of all possible values of alpha, beta, gamma if sin alpha=-1/sqrt(2), cos beta=-1/sqrt(2), tan gamma =-sqrt(3) , is

If a right angle be divided into three parts alpha, beta and gamma , prove that cot alpha = (tan beta + tan gamma)/(1-tan beta tan gamma) .

If cos alpha + cos beta + cos gamma = 0 and also sin alpha + sin beta + sin gamma= 0, then prove that: cos 3 alpha + cos 3beta + cos 3gamma = 3 cos (alpha + beta + gamma)

If 0 lt alpha lt beta lt gamma lt pi//2 , then the equation (x-sinbeta)(x-singamma)+(x-sinalpha)(x-singamma)+(x-sinalpha)(x-sinbeta)=0 has

OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS AND IDENTITIES-Exercise

The value of the expression is
Text Solution
|
If tan((theta)/(2))=5/2and tan((phi)/(2))=3/4, the value of cos(theta+...
Text Solution
|
If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gam...
Text Solution
|
If sin x+siny=3(cosy-cosx),then the value of (sin3x)/(sin3y), is
Text Solution
|
If cosx=tany ,cosy=tanz ,cosz=tanx , then the value of sinx is 2cos18^...
Text Solution
|
If k=sin^(6)x+cos^(6)x, then k belongs to the interval
Text Solution
|
The value of tan9^@-tan2 7^@-tan6 3^@+tan8 1^@ is equal to
Text Solution
|
If tan^(2)alpha tan^(2)beta+tan^(2)gamma+tan^(2)gamma tan^(2)alpha+2ta...
Text Solution
|
the value of e^(log(10)tan1^@+log(10)tan2^@+log(10)tan3^@....+log(10)t...
Text Solution
|
For what and only what values of alpha lying between 0 and pi/2 is the...
Text Solution
|
If (secA+tanA)(secB+tanB)(secC+tanC)=(secA-tanA)(secB-tanB)(secC-tanC)...
Text Solution
|
If pi lt alpha lt (3pi)/(2), then find the value of expression sqrt(4 ...
Text Solution
|
If alpha is an acute angle and sin(alpha/2)=sqrt((x-1)/(2x)) then tan ...
Text Solution
|
Find the Value of tan 82 1/2^@
Text Solution
|
The value of tan6^0tan42^0tan66^0tan78^0 is 1 (b) 1/2 (c) 1/4 (d)...
Text Solution
|
The value of cot36^(@)cot72^(@), is
Text Solution
|
The value of cospi/7+cos(2pi)/7+cos(3pi)/7+cos(4pi)/7+cos(5pi)/7+cos(6...
Text Solution
|
Find the value of cos(2pi)/7+cos(4pi)/7+cos(6pi)/7
Text Solution
|
The value of cos""(pi)/(9)cos""(2pi)/(9)cos""(3pi)/(9), is
Text Solution
|
Prove that cos ""(pi)/(9) cos ""( 2pi)/(9) cos "" (3pi)/(9) cos ""(4pi...
Text Solution
|