If f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(...

If `f(x)=x^(11)+x^9-x^7+x^3+1` and `f(sin^(-1)(sin8)=alpha,alpha` is constant, then `f(tan^(-1)(t a n8)` is equal to `alpha` (b) `alpha-2` (c) `alpha+2` (d) `2-alpha`

A

`alpha`

B

`alpha -2`

C

`alpha + 2`

D

`2 - alpha`

Text Solution

Verified by Experts

The correct Answer is:

D

`f(x) + f(-x) = 2`
Now `(sin^(-1) (sin 8)) = 3pi - 8 = y`
And `(tan^(-1) (tan 8)) = (8 - 3pi) = -y`
Hence, `f(y) + f(-y) = 2`
Given `f(y) = alpha`, we have `f(-y) = 2 - alpha`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

INVERSE TRIGONOMETRIC FUNCTIONS
CENGAGE ENGLISH|Exercise Multiple correct answer type|24 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
CENGAGE ENGLISH|Exercise Linked comprehension type|16 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
CENGAGE ENGLISH|Exercise Concept application exercise 7.6|9 Videos
INTRODUCTION TO VECTORS
CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos
JEE 2019
CENGAGE ENGLISH|Exercise Chapter 10|9 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(-1)(sin8))=alpha,alpha is constant, then f(tan^(-1)(tan8)) is equal to (A) alpha (B) alpha-2 (C) alpha+2 (D) 2-alpha

If int_0^1tan^(-1)xdx=alpha,t h e nint_0^(pi/4)tan^(-1)((2cos^2theta)/(2-sin2theta))sec^2thetadtheta is equal to: alpha (b) alpha/2 (c) 3alpha (d) 2alpha

("lim")_(n vec oo)"{"(n/(n+1))^(alpha)+sin (1/n)]^n (when alpha in Q ) is equal to (a) e^(-alpha) (b) -alpha (c) e^(1-alpha) (d) e^(1+alpha)

If cos^(-1)x-cos^(-1)y/2=alpha,t h e n4x^2-4x ycosalpha+y^2 is equal to 4 (b) 2sin^2alpha (c) -4sin^2alpha (d) 4sin^2alpha

If n=pi/(4alpha), then tan alpha tan 2alpha tan 3 alpha ... tan(2n-1)alpha is equal to (a) 1 (b) 1/2 (c) 2 (d) 1/3

Sum of roots of equations f(x) - g(x)=0 is (a)0 (b) 2alpha (c) -2alpha (d) 4alpha

if f(x)=(sin (x+alpha)/(sin(x+beta))),alpha ne beta then f(x) has

If sin 3 alpha =4 sin alpha sin (x+alpha ) sin(x-alpha ) , then

If the sum of squares of roots of equation x^(2)-(sin alpha-2)x-(1+sin alpha)=0 is the least, then alpha is equal to

The value of int_0^(pi/2) sin|2x-alpha|dx, where alpha in [0,pi], is (a) 1-cos alpha (b) 1+cos alpha (c) 1 (d) cos alpha

CENGAGE ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS-Single correct

If alpha in (-(3pi)/2,-pi) , then the value of tan^(-1)(cotalpha)-cot^...
Text Solution
|
tan^-1[(cos x)/(1+sin x)] is equal to
Text Solution
|
If f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(-1)(sin8)=alpha,alpha is const...
Text Solution
|
If sin^(-1) : [-1, 1] rarr [(pi)/(2), (3pi)/(2)] and cos^(-1) : [-1, 1...
Text Solution
|
If the difference between the roots of the equation x^2+""a x""+""1...
Text Solution
|
'solve tan ( sin − 1 ( cos ( sin − 1 x ) ) ) tan ( cos − 1 ( sin ( cos...
Text Solution
|
There exists a positive real number of x satisfying "cos"(tan^(-1)x)=x...
Text Solution
|
If tan^(-1)(sqrt(1+x^2-1))/x=4^0 then x=tan2^0 (b) x=tan4^0 x=tan1/4...
Text Solution
|
The value of (alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^3)/2sec...
Text Solution
|
tan(pi/4+1/2cos^-1x)+tan(pi/4-1/2cos^-1x), x!=0 is equal to
Text Solution
|
If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equ...
Text Solution
|
Prove that : 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1)...
Text Solution
|
If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then the value of asqrt((1-a^2))+...
Text Solution
|
lf asin^-1 x -bcos^-1 x=c,then asin^-1 x +bcos^-1 equal to
Text Solution
|
The solution of the inequality "log"(2) sin^(-1) x gt "log"(1//2) cos^...
Text Solution
|
sin − 1 ( sin θ ) > π 2 − sin − 1 ( sin θ ) find the range of θ
Text Solution
|
If |sin^(-1)x|+|cos^(-1)x| = pi/2, then x in
Text Solution
|
If (sin^(-1) x)^(2) - (cos^(-1) x)^(2) = a pi^(2) then find the range ...
Text Solution
|
The number of integer x satisfying sin^(-1)|x-2|+cos^(-1)(1-|3-x|)=pi/...
Text Solution
|
The number of solutions of the equation cos^(-1)((1+x^2)/(2x))-cos^(-1...
Text Solution
|