The set of values of a for which the equ...

The set of values of a for which the equation `Sin^4 x + Cos^4 x = a` has a solution is

Text Solution

Verified by Experts

The correct Answer is:

`1/2 le a le 1`

Topper's Solved these Questions

TRIGONOMETRIC FUNCTIONS AND IDENTITIES
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|19 Videos
TRIGONOMETRIC FUNCTIONS AND IDENTITIES
ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|24 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

Write the set of values of a for which the equation sqrt(3)sin x-cos x=a has no solution.

The set of values of 'a' for which the equation "sin" x ("sin"x +"cos" x) = a has real solutions, is

The set of values of lambda for which the equation "sin"^(4) x + "cos"^(4) x =lambda has a solution, is

The set of values of alpha for which the equation "sin"^(4) x + "cos"^(4) x + "sin" 2x + alpha =0 possesses a solution, is

The range of value's of k for which the equation 2 cos^(4) x - sin^(4) x + k = 0 has atleast one solution is [ lambda, mu] . Find the value of ( 9 mu + lambda) .

The range of the values of p for which the equation sin cos^(-1)(cos(tan^(-1)x))=p has a solution is

The range of values of p for which the equation sin cos^(-1) ( cos( tan^(-1) x)) = p has a solution is

The number of integral values of k for which the equation 7cos x+5sin x=2k+1 has a solution is (1)4(2)8(3)10(4)12

The equation sin^(6)x+cos^(6)x=a , has a real solution if

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Subjective Type Questions)

If m sin (alpha+beta) = cos (alpha-beta), prove that (1)/(1- m sin 2...
Text Solution
|
If alpha+beta+gamma=pi and tan((beta+gamma-alpha)/4)tan((gamma+alpha-b...
Text Solution
|
The set of values of a for which the equation Sin^4 x + Cos^4 x = a ha...
Text Solution
|
If a and b are positive quantities, (a gt b) find minimum positive val...
Text Solution
|
If a, b, c and k are real constants and alpha, beta, gamma are variab...
Text Solution
|
If x/("tan"(theta+alpha))=y/("tan"(theta+beta))=z/(tan(theta+gamma)), ...
Text Solution
|
Let f(x)=cos(a1+x)+1/2cos(a2+x)+1/(2^2)cos(a1+x)++1/(2^(n-1))cos(an+x)...
Text Solution
|
Eliminate theta from the equations tan(n theta+alpha)-tan(n theta+b...
Text Solution
|
If {sin ( alpha-beta)+cos(alpha+2beta)sin beta}^(2)=4 cos alpha sin be...
Text Solution
|
If A, B, C are the angle of a triangle and |(sinA,sinB,sinC),(cosA,...
Text Solution
|
In any DeltaABC, prove that Sigma (sqrt(sinA))/(sqrt(sinB)+sqrt(sinC...
Text Solution
|
If 2(cos ( alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)+3=0, prove tha...
Text Solution
|
If the quadratic equation 4^(sec^(2)alpha)x^(2)+2x+(beta^(2)-beta+1/...
Text Solution
|
If cos2theta=x+1/x, prove that 2cos3theta=x^3+1/x^3
Text Solution
|
If (cos theta(1))/(cos theta(2))+(sin theta(1))/(sin theta(2))=(cos th...
Text Solution
|
Prove that sum(k=1)^(n-1) ""^(n)C(k)[cos k x. cos (n+k)x+sin(n-k)x.s...
Text Solution
|
Determine all the values of x in the interval x in [ 0, 2pi] which sat...
Text Solution
|
Total number of solution for the equation x^(2)-3[sin(x-(pi)/6)]=3 is ...
Text Solution
|
In aDeltaABC, prove that Sigma(r=0)^(n)""^(n)C(r)a^(r)b^(n-r) cos ( ...
Text Solution
|
Resolve Z^5+ 1 into linear & quadratic factors with real coefficients...
Text Solution
|