If exp (sin^2x+sin^4x +sin^6 x........up...

If `exp (sin^2x+sin^4x +sin^6 x........`upto `oo)log_e 2` satisfies the equation `x^2 - 17x + 16= 0` then the value of `(2cos x)/(sinx+2cosx) ,(0 < x < pi/ 2)` is

`[(71)/(150),(61)/(99)]`

`[(71)/(140),(61)/(79)]`

`[(71)/(190), (61)/(130)]`

None of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

SEQUENCES AND SERIES
DISHA PUBLICATION|Exercise EXERCISE -1 : Concept Builder|60 Videos
RELATIONS AND FUNCTIONS-2
DISHA PUBLICATION|Exercise EXERCISE-2: CONCEPT APPLICATOR|30 Videos
SETS
DISHA PUBLICATION|Exercise EXERCISE-2 : CONCEPT APPLICATOR|30 Videos

Similar Questions

Explore conceptually related problems

If exp(sin^(2)x+sin^(4)x+sin^(6)x....... upto oo)log_(e)2 satisfies the equation x^(2)-17x+16=0 then the value of (2cos x)/(sin x+2cos x),(0

If 0ltxlt(pi)/(2) exp [(sin^(2)x+sin^(4)x+sin^(6)x+'.....+oo)log_(e)2] satisfies the quadratic equation x^(2)-9x+8=0 , find the value of (sinx-cosx)/(sinx+cosx) .

If exp [(sin^(2)x+sin^(4) x +sin^(6)x+.... oo)" In" 2] satisfies the equation y^(2)-9y+8=0 , then the value of (cos x )/( cos x+ sin x ),0 lt x lt (pi)/(2) , is

If e^(( cos^2 x + cos^4x+ cos ^6 x + ……..oo ) log_e 2) satisfies the equation t^2 - 9t + 8=0 , then the value of ( 2 sin x)/( sin x + sqrt(3) cos x) ( 0 lt x lt (pi)/(2)) is

If e^((sin^(2)x+sin^(4)x+sin^(6)x+...oo)ln2) satisfies the equation x^(2)-9x+8=0 find the value of (cos x)/(cos x+sin x),0

If exp [sin^(2)x+sin^(4)x+sin^(6)x+….infty)ln 2] satisfies the equation y^(2)-9y+8=0 and the value of (cosx)/(cos x+sin x),0 lt x lt (pi)/(2) is (1)/(1+sqrt(k)) then the value of k is _________

Statement -1:If exp {("sin"^(2)x + "sin"^(4)x + "sin"^(6)x +…)"log"_(e)2] " satisfie the equation" x^(2)-9x +8=0, "then " ("cos"x)/("cos" x + "sin"x) = (sqrt(3)-1)/(2), 0 lt x lt (pi)/(2) . Statement-2: The sum "sin"^(2) x + "sin"^(4)x + "sin"^(6) x + .... oo is equal to "tan"^(2)x

DISHA PUBLICATION-SEQUENCES AND SERIES -Exercise -2 : Concept Applicator

The value of 1/(2!) +2/(3!) +...+999/(1000!) is equal to
Text Solution
|
If a,b,c are in H.P.then which one of the following is true
Text Solution
|
If a,b,c and the d are in H.P then find the vlaue of (a^(-2)-d^(-2))/(...
Text Solution
|
The odd value of n for which 704 + 1/2 (704) + 1/4 (704) + ... upto n ...
Text Solution
|
If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6p!=1 , then the value o...
Text Solution
|
The harmonic mean of (a)/(1 - ab) and (a)/(1 + ab) is :
Text Solution
|
The sum of the infinite series(2^(2))/(2!) + (2^(4))/(4!) + (2^(6))/(6...
Text Solution
|
If a,b,c re in H.Pthen which one of the following is true
Text Solution
|
ABC is a right angled triangle in which /B=90^(@) and BC=a. If n point...
Text Solution
|
If S(1), S(2), S(3),...,S(n) are the sums of infinite geometric series...
Text Solution
|
If a is the A.M. of ba n dc and the two geometric mean are G1a n dG2, ...
Text Solution
|
If a ,ba n dc are in A.P., and pa n dp ' are respectively, A.M. and G....
Text Solution
|
The AM, HM and GM between two numbers are (144)/(15), 15 and 12, but n...
Text Solution
|
If the arithmetic geometric and harmonic menas between two positive re...
Text Solution
|
If exp (sin^2x+sin^4x +sin^6 x........upto oo)loge 2 satisfies the equ...
Text Solution
|
If L(1) = (2.02 +- 0.01)m and L(2) = (1.02 +- 0.01)m then L(1) + 2L(2)...
Text Solution
|
sum(k =1)^(n) k(1 + 1/n)^(k -1) =
Text Solution
|
The sequence {x(k)} is defined by x(k+1)=x(k)^(2)+x(k) and x(1)=(1)/(2...
Text Solution
|
If |x| lt 1,then the sum of the series 1 + 2x + 3x^(2) + 4x^(2) + .......
Text Solution
|
The sum of n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6^2+.... is...
Text Solution
|