Let alpha be a real number such that 0 ...

Let `alpha` be a real number such that `0 <= alpha <= pi.` If `f(x)=cosx+cos(x+alpha)+cos(x+2alpha)` takes some constant number c for any `x in R,` then the value of `[c + alpha]` is equal to (Note : [y] denotes greatest integer less than or equal to y.)

-1

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

TRIGONOMETRIC FUNCTIONS AND IDENTITIES
ARIHANT MATHS|Exercise Exercise For Session 1|10 Videos
TRIGONOMETRIC FUNCTIONS AND IDENTITIES
ARIHANT MATHS|Exercise Exercise For Session 2|10 Videos
TRIGONOMETRIC EQUATIONS AND INEQUATIONS
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos
VECTOR ALGEBRA
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|9 Videos

Similar Questions

Explore conceptually related problems

If alpha is a real number such that alpha>1, then the range of the function f(x)=(a^(x)-a^(-|x|))/(alpha^(x)+alpha^(|x|)) is

Q.Let p and q real number such that p!=0p^(2)!=q and p^(2)!=-q. if alpha and beta are non-zero complex number satisfying alpha+beta=-p and alpha^(3)+beta^(3)=q then a quadratic equation having (alpha)/(beta) and (beta)/(alpha) as its roots is

Let alpha and beta be real numbers and z be a complex number. If z^(2)+alphaz+beta=0 has two distinct non-real roots with Re(z)=1, then it is necessary that

Let f (x) = log _e (sinx ), ( 0 lt x lt pi ) and g(x) = sin ^(-1) (e ^(-x)), (x ge 0) . If alpha is a positive real number such that a = ( fog)' ( alpha ) and b = (fog ) ( alpha ) , then (A) aalpha ^(2) - b alpha - a = 0 (B) a alpha ^(2) - b alpha - a = 1 (C) a alpha ^(2) + b alpha - a = - 2 alpha ^(2) (D) a alpha ^(2) + b alpha + a = 0

Let alpha and beta be two real numbers such that alpha+beta=1 and alpha beta=-1 Let p_(n)=(alpha)^(n)+(beta)^(n), p_(n-1)=11 and p_(n+1)=29 for some integer n geq 1 Then, the value of p_(n)^(2) is

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)

Let alpha be a real number such that 0 <= alpha <= pi. If f(x)=cosx+c...
Text Solution
|
If alpha and beta are non-zero real number such that 2(cos beta-cos al...
Text Solution
|
Let -1/6 < theta < -pi/12 Suppose alpha1 and beta1, are the root...
Text Solution
|
The value of sum(k=1)^(13) (1)/(sin(pi/4 + ((k-1)pi)/(6))sin(pi/4 + (k...
Text Solution
|
Let f : (-1, 1) -> R be such that f(cos4theta) = 2/(2-sec^2theta for t...
Text Solution
|
The number of all possible values of theta, where 0 lt theta lt pi, f...
Text Solution
|
For 0 lt theta lt pi/2, the solution (s) of sum(m=1)^(6) cosec (the...
Text Solution
|
If sin^ 4 x/2+cos^4 x/3 =1/5 then
Text Solution
|
Let theta in (0,pi/4) and t1=(tan theta)^(tan theta), t2=(tan theta)6(...
Text Solution
|
cos(alpha-beta)=1a n dcos(alpha+beta)=l/e , where alpha,betamu in [-pi...
Text Solution
|
If 5(tan^2x - cos^2x)=2cos 2x + 9, then the value of cos4x is
Text Solution
|
Let fk(x) = 1/k(sin^k x + cos^k x) where x in RR and k gt= 1. Then f4(...
Text Solution
|
The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as (1) s...
Text Solution
|
If a Delta PQR " if" 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1 , ...
Text Solution
|
If A = sin^2x + cos^4 x, then for all real x :
Text Solution
|
Let cos (alpha+beta) = 4/5 and sin(alpha-beta)=5/13 where 0<= alpha,...
Text Solution
|
If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then which...
Text Solution
|
A triangular park is enclosed on two sides by a fence and on the third...
Text Solution
|
If 0 lt x lt pi and cos x + sin x = 1/2, then tan x is
Text Solution
|
In Delta PQR , /R=pi/4, tan(P/3), tan(Q/3) are the roots of the equati...
Text Solution
|