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How many solutions does the equation 5 ...

How many solutions does the equation `5 tan^-1 x+3 cot^-1 x=2pi` have ?

A

zero

B

Exactly one

C

Exactly two

D

Infinite

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH INSTITUTE-INVERSE TRIGONOMETRIC FUNCTIONS-ASSIGNMENT (SECTION - B)(OBJECTIVE TYPE QUESTIONS (ONE OPTION IS CORRECT))
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  3. How many solutions does the equation 5 tan^-1 x+3 cot^-1 x=2pi have ?

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  4. The equation sin^-1x-cos^-1x=cos^-1(sqrt3/2) has

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  5. If (tan^(-1) x)^2 + (cot^(-1) x)^2 = (5pi^2)/8 then x equals

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  6. Let cos^-1 (x/2)+cos^-1 (y/3)=theta and denote by f(x,y,theta)=0 the r...

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  7. If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi, then 1/(xy)+1/(yz)+1/(zx)=

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  9. If a,b,c are real positive numbers and theta =tan^(-1)[(a(a+b+c))/(bc)...

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  11. If alpha= tan^-1 ((sqrt3 x)/(2lamda-x)), beta= tan^-1 ((2x-lamda)/(lam...

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  12. The value of tan[1/2cos^(-1).sqrt5/3] is

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  13. If -1 le x le -1/2, then sin^(-1)(3x-4x^3) equals

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  15. Find the value of 4 tan^-1 (1/5) - tan^-1 (1/239)

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  16. cot^(-1)(sqrtcosalpha)-tan^(-1)(sqrt(cosalpha))=x, x, ge 0, then sin x...

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  17. If |cos^-1((1-x^2)/(1+x^2))| < pi/3, then x belongs to the interval

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  20. Let f(x) = cosec^-1[1 + sin^2x], where [*] denotes the greatest intege...

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