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The number of solutions of "cos"(2sin^(-...

The number of solutions of `"cos"(2sin^(-1)("cot"(tan^(-1)(sec(6cos e c^(-1)x))))+1=0` where `x >0` is

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The correct Answer is:
3
`cos (2 sin^(-1) (cot (tan^(-1) (sec(6 cosec^(-1) x))))) = -1`
`rArr sin^(-1) (cot (tan^(-1) (sec (6 cosec^(-1) x)))) = +- (pi)/(2)`
`rArr cot (tan^(-1) (sec(6 cosec^(-1) x))) = +-1`
`rArr tan^(-1) (sec(6 cosec^(-1) x)) = (pi)/(4), (3pi)/(4)`
`rArr sec(6 cosec^(-1) x) = +-1`
`rArr 6 cosec^(-1) x = +- 3pi, 2pi, +- pi`
`rArr cosec^(-1) x = +- (pi)/(2), +- (pi)/(3), +- (pi)/(6)`
`rArr x = 1, (2)/(sqrt3) , 2 " " ( :' x gt 0)`
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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Numerical)
  1. The solution set of inequality (cot^(-1)x)(tan^(-1)x)+(2-pi/2),cot^(-1...

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  2. If x=sin^(-1)(a^6+1)+cos^(-1)(a^4+1)-tan^(-1)(a^2+1),a in R , then th...

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  3. If the roots of the equation x^(3) -10 x + 11 = 0 are u, v, and w, the...

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  4. The number of values of x for which sin^(-1)(x^2-(x^4)/3+(x^6)/9)+cos^...

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  5. If the domain of the function f(x) = sqrt(3 cos^(-1) (4x) - pi) is [a,...

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  6. If 0<cos^(-1)x<1a n d1+"sin"(cos^(-1)x)+sin^2(cos^(-1)x)+sin^3(cos^(-1...

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  7. If tan^(-1)(x+3/x)-tan^(-1)(x-3/x)=tan^(-1)6/x , then the value of x^4...

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  8. If range of function f(x)=sin^(-1)x+2tan^(-1)x+x^2+4x+1 is [p , q], th...

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  9. If cos^(-1)(x)+cos^(-1)(y)+cos^(-1)(z)=pi(sec^2(u)+sec^4(v)+sec^6(w)),...

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  10. If the area enclosed by the curves f(x) = cos^(-1) (cos x) and g(x) = ...

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  11. Absolute value of sum of all integers in the domain of f(x)=cot^(-1)sq...

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  12. The least value of (1+sec^(-1)x)(1+c a s^(-1)x) is

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  13. Let cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x) be pi. If x satisfies the eq...

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  14. The number of integral values of x satisfying the equation tan^(-1) (3...

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  15. Number of solutions of equation sin(cos^(-1)(tan(sec^(-1)x)))=sqrt(1+x...

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  16. If the equation sin^(-1)(x^2+x+1)+cos^(-1)(lambda+1)=pi/2 has exactly ...

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  17. sin{2(sin^(-1)(sqrt(5))/3-cos^(-1)(sqrt(5))/3)} is equal to (ksqrt(5)...

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  18. The number of solutions of "cos"(2sin^(-1)("cot"(tan^(-1)(sec(6cos e c...

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