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If x in ( - pi/2, pi/2), then the valu...

If ` x in ( - pi/2, pi/2)`, then the value of `tan^(-1) ((tan x)/4) + tan^(-1) ((3 sin 2x)/(5 + 3 cos 2x)) ` is

A

`x//2`

B

`2x`

C

`3x`

D

`x`

Text Solution

Verified by Experts

The correct Answer is:
D
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ARIHANT MATHS-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single Option Correct Type Questions)
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  2. If x + 1/x = 2, the principal value of sin^(-1) x is

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  3. If x in ( - pi/2, pi/2), then the value of tan^(-1) ((tan x)/4) + ta...

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  4. If sin^(-1) x + sin^(-1) y = (2pi)/3", then " cos^(-1) x + cos^(-1) y

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  5. The value of cot (pi)/(4)-2 cot^-1(3) is

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  6. sin [ tan^(-1). (1 - x^(2))/(2x) + cos^(-1) . (1-x^(2))/(1 + x^(2))] i...

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  7. If cos^(-1) ((1-a^(2))/(1+a^(2)))- cos^(-1) ((1-b^(2))/(1+b^(2))) = 2 ...

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  8. If |cos^(-1) ((1 -x^(2))/(1 + x^(2)))| lt (pi)/(3), then

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  9. The value of cos^-1[cot(sin^-1(sqrt((2-sqrt3)/4))+cos^-1(sqrt12/4)+sec...

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  10. If tan^(-)(x)/(pi)lt (pi)/(3) x in N then the maximum vlaue of x is

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  11. If tan^(-1). (sqrt((1+x^(2))) - sqrt((1-x^(2))))/(sqrt((1+x^(2)))+sqrt...

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  12. Find the number of positive integral solutions of tan^-1 x + cot^-1 y ...

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  13. If cosec^(-1) ( cosec x) " and " cosec ( cosec^(-1) x) are equal func...

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  14. The value of underset(|x| rarr oo)("lim") cos (tan^(-1) (sin (tan^(-1)...

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  15. Complete solution set of (cot^(-1)x)+2(tan^(-1)x)=0, where [] denotes ...

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  16. Prove that sin7x + sin5x + sin3x + sinx = 4cosx cos2x sin4x

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  17. If asin^(-1)x-bcos^(-1)x=c , then asin^(-1)x+bcos^(-1)x is equal to

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  18. The number of integer x satisfying sin^(-1) |x -2| + cos^(-1) (1 -|3 -...

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  19. The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),...

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  20. Prove that (cos^3x - sin^3x)/(cosx - sinx) = (2 + sin2x)/2

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